My 7th grader refuses to put "50%" as the answer here because it's "not how my teacher taught us" and I won't tell him what 63/90 is as a percent as a matter of principle against a poorly worded question! (It should say "flipped an uneven coin" or "experimental probability")

[u/gailonmiles]

No matter how many times it landed on heads previously, the theoretical probability of the next flip is still 50%

[u/Alfredos_Pizza_Cafe_]

Reading this as a neutral party, I would think it's a trick question where the correct answer is really 50%. It should read "what percentage of flips came out heads" if they want a 70% answer

[u/Dry-Manufacturer7761 → u/Alfredos_Pizza_Cafe_]

This. It isn’t a math question, but a “learn to do word problems and remove extra information to answer the actual question.”

[u/ga239577 → u/Dry-Manufacturer7761]

I would agree assuming that is part of what’s being taught in the class. As worded, the answer is 50% … but if the class hasn’t been teaching kids to remove irrelevant information from the question, then the answer they’re looking for is probably 70%

[u/Dry-Manufacturer7761 → u/ga239577]

This is obviously second grade stuff. Logic should 100% be a part of the curriculum by this point. 2nd grade logic is all about saying “too much info, but here is the answer” or “not enough data and I cannot answer”.

[u/Wild-Guarantee-7357 → u/Dry-Manufacturer7761]

Seventh grade, not second grade. 7th graders should know that a coin is 50/50 no matter what

Edit: Everyone is missing the point of my comment again. OP’s child is in 7th grade, not 2nd. That is truly all I meant to say. I used “50/50 no matter what” as a shorthand for the fact that a 7th grader should understand these concepts, along with the nuance that comes along with them.

[u/Rattus375 → u/Wild-Guarantee-7357]

The odds of a 50-50 coin flipping heads 63 or more times in 90 flips is 1/10k. Odds are, this isn't a fair coin

[u/EmberOne1 → u/Rattus375]

But that's the cool thing about probability. Just because it only happens about 1 in 10k times doesn't mean it can't happen the first time, then the 9th time, then not again for 20k times. This has real world implications, too. Take, for example, when a supposed 100 year flood happens, and nobody decides to change any infrastructure to protect against damage or risk to lives next time, because they wrongfully assume that means it also won't happen again for another 100 years.

[u/-Reo- → u/Rattus375]

Too bad the question isn’t asking about the odds of the coin being unfair, then.

[u/bekroogle → u/Rattus375]

1 in 10k things happen all the time, though.

[u/ga239577 → u/Dry-Manufacturer7761]

My point is the answer the teacher likely considers “correct” depends on exactly what lesson or chapter they’ve been teaching. We all know the right answer is 50%.

The question is worded poorly - because unless there was added context in the teacher’s lessons - it appears the answer they’re expecting is 70%.

This leaves the student in a position where they have to guess which answer the teacher is expecting.

[u/GreatScottCreates → u/ga239577]

> This leaves the student in a position where they have to guess which answer the teacher is expecting.

Not to sound like a smart ass, but I feel like this sentence encapsulates my grade school experience

[u/ga239577 → u/GreatScottCreates]

I had to do this on some CompTIA exams for my Bachelor’s degree so it’s not just grade school.

Multiple questions were worded in a way where the right answer was dependent on the intent of the person asking the question.

[u/Marrsvolta → u/ga239577]

CompTIA isn’t pick the right answer, it’s pick the best answer, as in what they think the best answer would be to a problem with multiple solutions, and I would like to argue some of what they say is the best answer really isn’t. Fuck CompTIA

[u/DesignerPangolin → u/Dry-Manufacturer7761]

Putting aside that this is a poorly-posed question, learning to translate a natural language question into a formally rigorous mathematical expression is easily the most important part of mathematics education (at least until you get to real analysis). The rest is just mechanical data processing.

[u/Venusgate → u/Dry-Manufacturer7761]

It's not that either, it's a "how to argue with someone that gives you arbitrary data."

[u/philosifer → u/Alfredos_Pizza_Cafe_]

Technically if we are getting really pedantic, the question never states the coin is fair. It could be a 70% weighted coin

[u/FiggsMcDuff1 → u/philosifer]

I did poorly on a lot of homework by stating more information is required because of things like that. I wasn't trying to be an ass either, I just sort of missed the intent of the question.

[u/tidbitsofblah → u/FiggsMcDuff1]

If you state "more information needed, either the coin isn't fair and its the chance of heads is 63/90, or it's a fair coin and the other flips were unlucky and then it's a 50% chance" that should definitely give you full points on a question like this. Otherwise the teacher is a really bad teacher.

Just answering "more information is needed to solve this" without explanation is a bit more fair to not give you points for though.

I tell my students all the time that if they feel like there's information missing to be able to solve the problem, state what information they are missing and how that information changes the answer.

Edit: Sometimes they think that information is missing because they haven't fully understood some concept they need to know. But sometimes they are absolutely right that I've phrased the question ambiguously, realizing that might even warrant extra points.

[u/FiggsMcDuff1 → u/tidbitsofblah]

You make a great point. Often I did not elaborate, perhaps if I had I would've done better.

[u/tidbitsofblah → u/FiggsMcDuff1]

You probably weren't taught to do so, which is not on you.

[u/oldsnowcoyote → u/FiggsMcDuff1]

So much of school was learning what the teacher wanted.

[u/cur10us_ge0rge → u/oldsnowcoyote]

Almost like it was training you for work.

[u/thomsenite256 → u/Alfredos_Pizza_Cafe_]

put 50 and fight with the teacher when its marked wrong would be my answer

[u/RandomWordCombo9632 → u/thomsenite256]

Careful. You might get the teacher, the principal and the school district to declare that the odds for heads when flipping a coin is actually 70%

Just like how fire produces wood and oxygen.

for context:

In Firewood combustion:

1. Which of the following statements is correct?
   

a. The cellulose and oxygen products indicate that this combustion reaction is endothermic.

b. The heat and light products indicate that this combustion reaction is exothermic.

c. The cellulose and oxygen products indicate that this combustion reaction is exothermic.

d. The heat and light products indicate that this combustion reaction is endothermic.

Clearly A and D are false. It says endothermic, meaning it pulls in heat.

C is obviously incorrect. Cellulose and oxygen are consumed not produced during combustion.

The answer is B!

Teacher: No. The answer is C because light is not always a result of combustion.

??????????????????????????????????????

And cellulose and oxygen are?!

Not only did the teacher double down when the parents protested, the principal triple downed by backing the teacher. And the school district quadrupled down by stating the teacher was correct in their grading.

It took regional headlines to make them reverse the decision and regrade.

Never underestimate people's ability to be really stupid.

[u/CallMeRudiger → u/RandomWordCombo9632]

The story drew international attention to the district, with emails sent from chemistry experts from several countries, former and current teachers, parents and at least one cannabis business owner who called the teacher’s combustion answer “incontrovertibly false” and the length of the district’s investigation “embarrassing.”

Man am I glad they made sure to include all of the combustion experts who reached out.

[u/RandomWordCombo9632 → u/CallMeRudiger]

Hey man... you gotta know how things work to get the good good ya knwo?

[u/_______no-------name → u/RandomWordCombo9632]

Wow, that is some next level self-fellatio shit. I am glad I have never met profs as dumb and egotistical as that.

[u/pjhsv → u/RandomWordCombo9632]

  Teacher: No. The answer is C because light is not always a result of combustion.

How often is oxygen a product of combustion?

Even if the teacher is right, the closest possible answer would be "none of the above"

[u/eneug → u/RandomWordCombo9632]

Wow this is insanely pathetic. If the science teacher can’t instantly see that that answer is obviously wrong, they should not be teaching science. I would be furious if my kid were being taught by someone that science illiterate. And just plain stupid — their logic about “combustion doesn’t always produce light,” even if it were true, does not affect the answer!

And there were 5 other questions they got wrong as well?? So the middle school science teacher would not ace their own exam? They should straight up be fired.

[u/Enigma_Stasis → u/thomsenite256]

https://giphy.com/gifs/c9tVMERePnnDW

[u/TheGrandWhatever → u/Enigma_Stasis]

Education sponsored by Kalshi. Is the coin flip odds 70%? Let's bet on it

[u/JHtotheRT → u/Alfredos_Pizza_Cafe_]

In math, you often specify the coin is fair, you don’t just assume it. ‘Sofia slipped a fair coin’ would be the wording to avoid ambiguity. You can’t just assume à coin is fair without that. In fact it’s very likely this coin isn’t fair given the results, but that’s obviously wel outside the scope of a second grade math problem.

[u/MuhfugginSaucera → u/JHtotheRT]

People are getting caught up on the coin part. We should ignore the coin and treat the problem like a math problem. The object is generally irrelevant, the math is not.

The person who wrote this word problem shouldn't have chosen a coin. The world problem and the answer are the same regardless of the object being used.

[u/doesntbite_much → u/Alfredos_Pizza_Cafe_]

https://giphy.com/gifs/2sddZ3k7yxiVWpFdH3

[u/Burger_Queeph → u/Alfredos_Pizza_Cafe_]

It really depends how clever the teacher is. Some teachers think they're the center of the universe and what they meant to ask is just as good as what they actually wrote down. It could be either case.

[u/roosterSause42 → u/Alfredos_Pizza_Cafe_]

That’s the way I read it too.

It’s a lesson in recognizing irrelevant information.

The only info needed is the question “What is the probability of landing in heads” and that a coin has 2 sides, heads and tails.

Ignoring landing on edge and the bias of a flipped coin to result in the side that was up when flipped: the answer is 50%

[u/MenacingScent]

Teach your child to provide every possible answer to an unfinished question.

example

"If you're asking the theoretical probability, then 50% always no matter what. Two sides of the coin, assuming both sides are equal in weight, you have a 50% chance of either."

"If you're asking probability based on previous outcome, then there is a 70% chance of it landing on heads."

This is how you do it practically in the real world. Not everyone can get their point across, humans error exists inside and outside of the classroom, and if you provide an answer based on what you think without ensuring it's both said correctly and understood correctly, then your answer could be wrong. If you provide both answers and state you're not quite sure which way the question was meant, then there's no way you can be wrong and you should be commended for taking the initiative and making the extra effort to provide the correct answer regardless.

Literacy is dropping, also. Schools don't enforce it nearly as much anymore and the internet has taken a toll on kids' understanding and interpretation of it, to the point where new generation teachers are half as qualified as those before them but they're all we have, so we as parents have to teach our children to be critical thinkers and to fill in the blanks where other people may lack, even if it's not their fault.

[u/Avery-Attack → u/MenacingScent]

I did this in a college class (it was an anthropology class rather than math, so I would argue good wording is even more important) and ended up with points docked because my professor thought I was being sarcastic or pedantic or something. I'd still tell my kid to do it and back them up if they got the same response.

Also, I need to defend teachers a little bit. I was going to school for elementary and special education and at least in my state and school I can say that we were taught about the literacy crises, the reading wars, how important it is to teach critical thinking and having broad methods for broad learning styles. But it's not feasible for a teacher to be able to teach it all to 20-some to 30-some kids in the time they have during the day. When it comes to raising a well-rounded generation both teachers and parents need to be involved, but these days it's usually one or the other and in worst cases no one is teaching a child how to actually THINK. I think I get what you're saying, though. It's systemic and the current momentum is continuing to fall.

[u/PapaFedorasSnowden → u/Avery-Attack]

I'm all for defending teachers. The work they do is incredibly important and undervalued. But questions should be worded clearly and with no ambiguity. If there is more than one valid way to interpret a math question, you as a teacher have not done the absolute basics of your job.

I am autistic, I spent my entire life (even my adult life) dealing with badly worded questions from people who should know bette. Being an out of the box thinker, I could always see there was more than one possible answer. Basic synthax and semantics are very simple. I would say this makes me irrationally angry, but I think my anger is perfectly rational.

I remember in fourth grade, we had an exam on reptiles and one of the questions was "which order of reptiles can stay very long without eating?" I answered Squamata (snakes), as it is well known many species of snakes eat weekly or even monthly (see anacondas). The teacher wanted crocodillia and would not accept my answer even after I brought a college textbook and my biologist grandmother to confirm what I said. It's been 18 years. It was the only question I got "wrong". I still hate her. It was one of the moments that marked me and killed my innocence. Were it not a lot of luck, this could have killed my curiosity and my drive to learn, as I saw this exact kind of thing do to many, many bright people.

[u/Avery-Attack → u/PapaFedorasSnowden]

Yes, I think having properly worded questions is a part of being a good teacher. The good teachers I've had would give credit back if a student came to explain their reasoning to them. I am also autistic and understand your story completely. I wouldn't be over it either, honestly, especially after trying to explain. Teachers have to be flexible and willing to talk and be wrong and your teacher failed in that. I wish I were still interested in elementary teaching because that's the sort of thing younger kids need. I had a few times where my light would go out because a teacher was careless or didn't notice something. I didn't become interested in learning again until college when it was finally my own choice to do it. The fact that you tried to change your teacher's mind is pretty amazing, honestly. I never would have had the gumption to do that.

I just had to do a quiz last week that had "multiple answers that are correct but only one BEST answer" and it drove me crazy. It's a ridiculous way to organize questions.

[u/BIGBADLENIN]

That has a p-value of 0.0002 given a fair coin, so we can reject the null-hypothesis (the coin is fair) and so our best guess is that that the probability for heads is closer to 63/90

[u/cheese_is_available → u/BIGBADLENIN]

In other words, given the empirical data we have, the probability for heads has 95% chance of being between 60,5% and 79,5%, 99% chance of being between 57,6% and 82,4%, and 99,99% chance of being between 51,2% and 88,8%... (using wald interval). Also there's a 100% chance that this is absolutely not the answer the teacher wanted.

[u/smilingcube → u/cheese_is_available]

Plot twist, the child is homeschooled.

[u/Manlysideburns → u/BIGBADLENIN]

This just rocketed me back to stats class in college. Had an amazing prof

[u/Yarwi1 → u/BIGBADLENIN]

Saying "flipped a *fair* coin" is one of the most important things with stating these problems, so you know the coin is *supposed* to be 50/50. Without that, you have no reason to assume it is fair, especially with these odds. So the correct answer *should* be 70% here.

[u/TibialTuberosity → u/BIGBADLENIN]

From a definitional perspective, I know what you're saying, but that sentence also makes absolutely no sense to me whatsoever because to this day stats just does not mesh with my brain.

[u/Cruel1865 → u/TibialTuberosity]

In simple terms, theres a high chance that the coin is not equally balanced and thus not fair. So the probability of getting heads is not in fact 50% and instead 70%.

[u/AllHailKingJoffrey → u/TibialTuberosity]

If my understanding of statistics is correct, the statement says that a fair coin would give 63 heads out of 90 throws in 0.02% of the time. That is such a low percentage that we conclude that the assumption of 'fair coin' is wrong. In most cases we can reject the null hypothesis if the p-value is less than 2.5%.

[u/Dodezv → u/AllHailKingJoffrey]

Yes,  but it is 63 heads or more, since you would also believe it is not fair if they were even more heads. Plus, 63 tails or more would be equally exceptional, so we would add that, too.

It all depends on whether your suspicion is that your coin is manipulated 

• to give close to 63 heads or
• to give many heads or
• to be not fair

[u/AllHailKingJoffrey → u/Dodezv]

Yes, it is coming back to me now, it has been a while since I did the statistics. The 63 tails scenario would be the other end of the bell curve, with an equal cutoff of 2.5%, giving a confidence level of 95%. It was implicit in my original comment, but it could have been stated more clearly.

[u/gazow → u/AllHailKingJoffrey]

whats the probability that your understanding of statistics is correct thought?

[u/PopeRaunchyIV → u/BIGBADLENIN]

Better yet, be Bayesian, put a prior over the probability of heads with much of the density near 0.5 to represent our domain knowledge that most coins are nearly fair, and look at the posterior probability its near 0.5

[u/taiteilijahonppeli]

Smart-ass answer most likely would be like "While probability of heads is always 50% on even coin, it appears to be 70% on this short experiment."

[u/Purple_Onion911 → u/taiteilijahonppeli]

I did something like this in middle school and got a bad grade lol

[u/ncocca → u/taiteilijahonppeli]

Yes! Give the teacher all the information to show you understand the concept but that the question is confusing. This is the kind of shit we would answer in my engineering classes when questions weren't worded well. Which was rare, because our professors were usually quite deliberate about wording things explicitly. 

In engineering you get used to writing out your assumptions when answering questions. 

[u/Fluffy-Support5828 → u/taiteilijahonppeli]

You deserve an award, because I would probably answer the question that way, even in middle school😂😂

[u/Rukir_Gaming]

"What is the current percentage of heads to tails flipped"

There fixed the prompt

[u/T_RAYRAY → u/Rukir_Gaming]

What is the historical actual result of heads to tails flips for these specific 90 coin flips.

[u/ganbramor → u/Rukir_Gaming]

“Percentage of heads out of all flips.” If you’re going to say “to” then it’s “ratio of heads TO tails.

[u/DesignerPangolin → u/Rukir_Gaming]

If the coin is fair, the probability of getting a result as or more extreme than 63/90 is p=0.0188, so by the typical statistician's cutoff of alpha=0.05, we'd reject the null hypothesis that the coin was fair and accept that the coin's sampled tilt of 0.7 is an unbiased estimator of the true mean. If you were a particle physicist, you'd accept the null hypothesis as they use a more rigorous standard of five sigma (alpha=2.87*10^-7), so the answer would be 0.5. If you were a parent in whatever state approved this textbook, I would accept the hypothesis that you deserve to be mildly infuriated.

[u/HudeniMFK → u/Rukir_Gaming]

Yes but still no,

[u/HarbingerML]

Just to clarify, you are saying you refuse to tell them what 63/90 is as a percent out of principle .. so your child is not capable of expressing this fraction as a percent but your main concern is they know the general probability of a coin flip (assuming the coin is a fair one - which incidentally is stated nowhere in the problem)

Maybe you should worry a little more about helping your son with more elementary skills and a little less about self-congratulatory gotcha moments.

[u/gibbylewd → u/HarbingerML]

Reminds me of that dude who refused to teach his (young) kid how to use a can opener when she was hungry so she could learn critical thinking skills, and he wrote a pseudo-intellectual essay on twitter about how deep and philosophical he is

[u/Naynayb → u/gibbylewd]

bean dad! turned out to have said some antisemitic things that didn’t resurface when he ran for city council, but did when he became twitter’s main character of the day. simpler times

[u/drbeerologist → u/gibbylewd]

Good ol Bean Dad

[u/commentsandopinions → u/gibbylewd]

Sounds familiar...

[u/helinze → u/commentsandopinions]

But not too familiar? 

[u/Tumleren → u/helinze]

But not too not familiar

[u/miaomiaou → u/HarbingerML]

I mean, hopefully the child was taught how to calculate a percent from a fraction as a part of the lesson. Hopefully the child is able to actually do the calculation without their father simply telling them that percentage.

[u/ProfDFH → u/HarbingerML]

The infuriating part is not the math question. The infuriating part is the OP is an idiot who thinks he’s clever.

[u/Opus_723 → u/HarbingerML]

Kid understands this is just a lame prompt to get him to calculate a percentage and is trying desperately not to get a bad grade because his dad wants to look smart.

[u/theRealhubiedubois → u/HarbingerML]

I'm glad someone else said this. It's so sad these kids are growing up with parents trying to own their kids' teachers instead of focusing on what their kid is supposed to be learning. Obviously our education system needs a LOT of work but most of the time these posts end up revealing more about OP than about the kid or their teacher. Like in this case, OP obviously misunderstood the point of the question because they leapt to the conclusion that the "coin" being used is a 50/50 coin. The critical thinking is LACKING.

[u/Bad-Luck-Guy]

Unfortunately your kid is probably right, that’s probably the answer to this stupid question. I remember being frustrated by questions like this in school. The one time my Dad tried to help me with math I failed the assignment because he insisted I do everything differently than we were learning in class.

[u/Rough_Possession_ → u/Bad-Luck-Guy]

I had done science homework multiple choice, I asked the student teacher, that was in the same class a clearifing question about one question I couldn't answer. They looked at all my awnsers and made me "correct" half of them. Each correction she provided an explanation that sounded logical but was actually made up. I would have gotten an 87% on that homework but ended up with a 63% the worst part was we spent hours correcting everything because it took me a long time to understand her false explanations. I finally thought I strongly understood the material then I got the grades back

[u/red__dragon → u/Rough_Possession_]

Each correction she provided an explanation that sounded logical but was actually made up.

This was the entirety of college physics classes for me, but it was the professor's numbers. I love the concepts but apparently hate the math problems for physics.

[u/qimerra → u/Rough_Possession_]

Ugh you just flashed me back to an English teacher who failed me on an essay delving into the themes of a story because "THAT'S NOT WHAT IT WAS ABOUT!" (She actually wrote it in caps lol.) Her intellectual poverty aside, I'm pretty sure my interpretation was closer to the author's intentions.

In a way though these lessons do prepare us for what life out in the world is like.

[u/SerendiPetey → u/Bad-Luck-Guy]

My dad used to say: "The coin has no memory." Thus 50/50.

[u/AradynGaming → u/SerendiPetey]

Your dad is correct that a coin doesn't have a memory, but it likely has a weight imbalance. It is extremely rare that something is so perfectly balanced that it will have perfect 50/50 odds. Vegas/casinos routinely kick out people who are quick figure out the imbalance of dice/roulette wheels/etc because it removes the house odds.

The dice might not be able to remember that they landed on "6" last time, but the uneven weight distribution, causes them to want to stop just a little bit more every time the 6 comes up.

[u/Avocadonot]

Man reading these comments is dismal

[u/Diels_Alder → u/Avocadonot]

Probability is tragically misunderstood.

[u/raz-0]

Your kid has learned the important lesson that you get farther answering the question intended then telling people who can make your life suck that they are morons. The fact they are morons will not help your situation.

[u/RusDaMus → u/raz-0]

You probably meant "than", right? In your version, you're still telling people that they're morons.

[u/rex5k → u/RusDaMus]

Above poster has learned the important lesson that your grammar needs to be perfect if you plan on insulting anyone's intelligence in any way.

[u/Rocket_safety → u/rex5k]

[u/Stormsurger → u/raz-0]

There's also a different lesson to learn. Often people don't say exactly what they mean because they made a mistake, or were imprecise, or didn't fully think the words they were going to say through. Being able to understand what they mean with their words instead of taking the words at face value is an important skill.

[u/Nilmerdrigor]

The hidden complexity of this question is kinda crazy for a a 7th grad homework. You'll have to go into confidence interval and more lol.

[u/Resident_Step_191 → u/Nilmerdrigor]

Lol I was thinking that too, but I actually think “experimental probability” is what the teacher’s most likely going for. Apparently it’s a common topic in some schools around 7th grade: you are just expected to divide the number of successes by total number of attempts.

Ideally, if that’s what the teacher was going for, they would say something like “what is the experimental probability of landing on heads” rather than just “what is the probability.”

As stated, it really seems like you either need to assume the coin is fair (even when there is good reason not to) or perform some formal, undergrad-level hypothesis test or maximum-likelihood estimator. I grade this teacher a D

[u/DrunkenVerpine → u/Nilmerdrigor]

Funny thing my mind went to... there is no assumption provided the coin is fairly balanced, so 63/90 is the best approximation if you're not sure its fair.

Certainly there are counter arguments just sharing where my head went, which aligns with your comment about the depth of it.

[u/35point1 → u/Nilmerdrigor]

I wouldn’t call it hidden complexity as much as it is a poorly worded question

[u/LukeLJS123]

μ=0.7 and σ=0.04830, so x=0.5 has a z-score of -4.1408, so the p-value is 0.00001730, and with α=0.05, we can assume that this is not a fair coin

i took stats in 2023 so don't come for me if i should have assumed that the mean is 0.5 instead of 0.7, my point still stands that this is almost definitely not meant to be a fair coin

edit: i think we should assume the coin is fair and do the math based on that, since that is what we are assuming. the null hypothesis is that the coin is fair, so that should be our μ, 0.5

so when μ=0.5 and n=90, σ=0.05270, and with x=0.7, z=3.795, so P(z>3.795)=0.00007382, which still falls well below α=0.05, thus the coin is most likely unfair

[u/Malev0 → u/LukeLJS123]

This right here. Never said the coin was fair.

Gotta Law of Large Numbers that shit.

[u/ace-mathematician]

In probability, there are two calculation approaches: classical and empirical. The classical approach is based on the equally likely outcomes of H and T, and we calculate the theoretical probability as 1/2.

Empirical probabilities are based on the results of a performed probability experiment. In this case, the empirical probability of heads is 63/90.

Is this a poorly worded question? Maybe. Depending on the grade level, the students may not have been exposed to all the nuance yet.

[u/InfinitelyRepeating → u/ace-mathematician]

This was my thought.

It could be that this question is from a worksheet for a lesson on experimental probability, so by context, that's what the teacher wants to do.

Furthermore, this question opens the door to all kinds of related topics like theoretical vs experimental probability, simulation and (baby steps into) confidence intervals and hypothesis testing.

We don't have enough information from this post to know, and too many people (including the OP*) are high-5ing themselves over how clever they are to try to find out.

*When I say OP, I mean the person who posted the picture, not the very nice person I'm responding to.

[u/ExamplePractical1981]

We had a math test in 7th!!! grade. Our teacher was a douche. The question was about parking a car for 137 minutes and calculating the cost if an hour cost €5. The answer was €15 because every hour started was charged in full. HOW THE FUCK WERE WE SUPPOSED TO KNOW THAT?! We were in 7th grade!!! This shit is STILL fucking me up 20 years later 😂

https://giphy.com/gifs/vmgJEo71lzE85Qy8pe

[u/Ancient_Yellow_709 → u/ExamplePractical1981]

Bro, I had the same type of teacher except they asked how long did some Roman guy lived. I had, of course, memorized the birth and death dates as instructed. I had been studying for the PSAT in 7th grade (there was some reason they had us take it early) and they gave us the tip of not falling for the trick of forgetting inclusive values.

So I think to myself "How many years was he alive? Yeah, that's probably inclusive, right? They didn't ask how old he was when he died, which would require him having completed the birthday cycle for that year so he must be being tricky like that." So I write out the dates I memorized, subtract them, and add one, showing my work.

The teacher marks it fully wrong. I go argue with him, point out that I showed my work and that his question was unclear and point out my logic for answering that way. His answer was that most people answered it correctly and I got a high enough grade already. F you, Mr. B. If you're alive 2000-2010, you're alive in 11 years.

(He also screwed me over in a schoolwide geography bee by assigning the one other girl's mistakes to me and the principal had to intervene; oddly enough, the girl went on to win...the girl's mom worked at the school and he was friends with her.)

Edit: typo

[u/Myclarinetto → u/Ancient_Yellow_709]

But you are wrong tho. He didn't ask "In how many years was he alive", but "How many years was he alive", therefore asking for the age

[u/Ancient_Yellow_709 → u/Myclarinetto]

But they didn't tell us his birthday! They gave us his birth year and death year in the textbook, as mentioned.

There was no reasonable way for us to know how old he actually was (this was when Wikipedia wasn't trusted and looking stuff up in encyclopedias was onerous, since we'd be unlikely to have a book on this guy in our school library).

So my interpretation was at least as reasonable an interpretation. And I included the dates he was born and died. I clearly knew the material that was being tested. That teacher was a prick to give me zero points even if he disagreed with my math. He'd give other students who did zero work but who had rich parents or who worked for the school partial credit for getting stuff wrong without showing work.

[u/HungryCowsMoo]

I apologize if i sound harsh, but i think you should drop your principles and give your 7th grader the help he is asking for.

I agree the question is ambiguous especially considering he is learning about theoretical and experimental probability, but if we want to be sticklers no where in the question does it state the coin is fair.

He’s in 7th grade, being wrong or right is not the primary goal, the primary goal is to learn. He’s asking for help on how to calculate 63/90 as a percentage and you are refusing to teach him. I think you’re right to not “tell” him that it’s 70%, but wrong to not guide him on how to figure that out for himself.

[u/TheClimateDad → u/HungryCowsMoo]

I’d also add that the probability of a fair coin landing on one side 63/90 or greater times is 1 in 10,652, or a 0.0094% chance. The math would illustrate that the coin is almost certainly an uneven coin, so the big brain answer here is the same as the basic one - the coin has demonstrated a 70% probability of landing heads.

[u/throwaway111222666 → u/TheClimateDad]

that's really not it either. you can't get a real probability out of this at all, at best you get a confidence interval. the coin could easily be 65%, or 75

[u/uwill1der]

This is where you learn from your 7th grader the difference between meaning and intention

[u/TealCatto → u/uwill1der]

Are you saying that it's right to reject a very clearly expressed statement and replace it with what you think the speaker actually meant?

[u/TheSpaceNeedle → u/TealCatto]

The curtains were blue

[u/BootVillain → u/TealCatto]

And THAT is the typical redditor lmao

[u/stateofsirens]

It may not be a 50% chance if the coin isn't noted to be fair. The probability of the next flip being heads is 50% only if there is actually a 50% chance of it happening on all flips. Just because the trial outcomes are not influenced by previous outcomes does not mean that it's automatically a 50% chance.

[u/Biochemicalcricket → u/stateofsirens]

Also, with sufficient sampling you can prove it isn't 50/50 but over 90 flips you're still WELL short of that proof, but one would be fair to assume over 2/3 is a major deviation from 50/50. It's improbable that the coin is balanced even at that without additional info as presented.  

Really shit question to try to prove a point on without reworking it

[u/Rattus375 → u/Biochemicalcricket]

1/10k odds for a fair coin to be that imbalanced after 90 flips

[u/ByeGuysSry → u/Rattus375]

1 in 5k. I think you mistakenly calculated the odds of getting heads at least 63 times, when you should instead calculate the odds of getting heads at least 63 times OR tails at least 63 times

[u/Xezron2000 → u/ByeGuysSry]

Damn, this guy fucks in math

[u/SportResident8067 → u/stateofsirens]

Teach them how to calculate a standard deviation and the real answer is 70% with an error bar.

[u/The24HourPlan]

Is it meant to mean that it's an unfair coin?

[u/TheRealMitchConnor]

I just flipped a quarter 10 times and got heads 9 out of 10 times. It's just happenstance. The probability is still 50% every time... not 90%.

[u/BentGadget → u/TheRealMitchConnor]

I just flipped a coin ten times and got tails 9 times out of ten. I think our coins are quantum-entangled.

Either that, or one of us is faking the data.

[u/TheRealMitchConnor → u/BentGadget]

Noooo you see. That's likely. That's chaos.

https://giphy.com/gifs/11FiDF2fuOujPG

[u/BentGadget → u/TheRealMitchConnor]

I just can't believe my results are real. Mostly because I don't have a coin.

[u/Stompya → u/BentGadget]

78.4% of all statistical data is made up on the spot

[u/Resident_Step_191 → u/TheRealMitchConnor]

The probability of flipping 63 heads out of 90 with a fair coin is 0.00556% or about 1 in 20 thousand.

By comparison, you flipping a fair coin 10 times and getting 9 heads has a probability of about 1% or 1 in 100.

Both unlikely events, but of completely different orders of magnitude

[u/adxn40l → u/Resident_Step_191]

As you say, this is with a "fair" coin. The problem does not state that it is such.

[u/Happy-Plant458]

it should definitely be asking what percent of the results was heads but i feel thats an argument you should be having with the teacher not your kid

[u/RelativeThese2634 → u/Happy-Plant458]

How else am I going to get fake internet points tho!!!

[u/Captain-Griffen]

P value of 0.000188. Don't think that's a fair coin toss.

[u/Rikki-Tikki-Tavi-12 → u/Captain-Griffen]

This. If I have it right, the chance of this coin being fair is about 1 in 15k

[u/PissMissileTopTitty → u/Rikki-Tikki-Tavi-12]

So glad to see some sanity in this thread. Sure, it's a gr7 class, still very much worth pointing out that the information provided strongly suggests the coin is weighted

[u/developer-mike → u/Captain-Griffen]

Yes, and in math courses you'll often see "fair coin" if you're supposed to assume 50%. This question does not say "fair coin."

[u/gailonmiles]

Fwiw we finished the homework writing 70%

[u/TankApprehensive3053 → u/gailonmiles]

Update when it gets graded.

[u/TheCunningRabbit]

As a math teacher with years of teaching this grade in experience, this needs clarification. Is the teacher requesting the theoretical probability or the experimental.

The theoretical probability is 1/2 or 50%. The experimental probability is 63/90 or 70%. Without knowing the type of probability that the teacher wants you can't be sure which answer the teacher wants.

[u/FashionableLabcoat → u/TheCunningRabbit]

Thank you. I remember arguing with my own gradeschool math teacher about this when I was in school— theoretical vs experimental probability needs to be specified!

[u/33rpm_neutron_star → u/TheCunningRabbit]

As a statistician, I have never heard anyone call this “theoretical” and “experimental” probability. You might estimate the probability based on data and/or some priors, and you may hypothesize a particular value, or consider a range of models to compare with differing values, but “probability” in this context is generally thought of as a population quantity (aka, always in some sense “theoretical”). 

[u/TheCunningRabbit → u/33rpm_neutron_star]

It's part of the standards as 7.sp.c.6.

While at the high school and beyond level you are extremely correct, at the middle school level it is helpful for students to break down probabilities this way. One such reason is understanding the gamblers fallacy. Another is for being able to discover when their calculation of "theoretical" probability is wrong. It may be best to think of it as a stepping stone towards a deeper understanding or a better understanding of how things work.

[u/DirkPitt106 → u/TheCunningRabbit]

With the citations. Maybe there's instructions at the top of the homework worksheet that specify if the homework is about theoretical or experimental probability. But OP did specifically use those terms in their post so we can theoretically rule out that possibility.

[u/Virtual-Goose1243]

Here is why your son is giving a better answer. Knowing nothing other than the outcome, one can ask reasonably "is this a fair coin?" A fair coin (50% heads and 50% tails) in N independent flips follows a binomial distribution.

For a fair coin flipped 90 times:

• Exactly 63 heads: 0.021% (about 1 in 4,762).
• 63 or more heads: 0.0321% (about 1 in 3,116).

Technically speaking, this outcome is possible for a fair coin, but statisticians ask "what is the likelihood of this outcome under our proposed hypothesis?" In this case, the null hypothesis is that it is fair. Assuming the coin is indeed fair, the likelihood of observing that coin flip is astronomically small. Statisticians use the likelihood of an observation under the null hypothesis to draw conclusions on whether or not to accept or reject the null hypothesis. For a typical situation like this, we would say an observation whose likelihood of occuring is less than 5% is generally evidence supporting rejection of the null. What we observed here was 78 times less likely than what scientists would typically use to reject.

So it's safe to say to conclude the coin isn't fair and the probability isn't 50%.

[u/Virtual-Goose1243 → u/Virtual-Goose1243]

A standard 95% confidence interval around this observation is 59.8% to 78.5%, meaning the true rate of heads is (likely) in that interval. So any answer in between there is reasonable, and the maximum likelihood estimate (aka most likely to be the true rate of heads) is exactly what your son or daughter wrote.

[u/gailonmiles]

A few clarifying points while we wait for the grading of the assignment tomorrow!

1) the homework was kind of a multi topic review. Other questions included fractions, event likelihood, number lines, frequency, a question about number of expected results by rolling two dice, and this question. The homework title is "warm up week of October 12" so no implication of what probability this question should be.

2) So obviously next step was look at what he was working on for the week and LITERALLY the first two worksheets behind this homework one is titled "theoretical probability" and the second is titled "experimental probability." I kid you not.

So I'm not sure any more of what answer the teacher is expecting but my original frustration is still focused on that this is an ambiguous and confusing question.

Update tomorrow promised!

[u/bren_derlin → u/gailonmiles]

Just write both answers. The theoretical probability is 50%, the experimental probability is 70%. It’s not like it’s multiple choice.

[u/Comprehensive-Ease10 → u/gailonmiles]

Yeah, as a middle school math teacher myself, that's a terrible question LOL.

The probability (suggesting future) of it landing on heads-- or tails-- is of course 50% (I don't think we can reasonably assume that it's an uneven coin, especially with a relatively small sample size and unless it was explicitly stated).

However, the way the question is worded and based on the information given, in combination with the other things they are learning about, suggests that the teacher might be looking for the 63/90 as the fraction that demonstrates the previous results, even though that's not a probability in this case.

That's disheartening to see. Best of luck to your 7th grader. I would give them an A for discussing it with their parents and having what sounds like a lively math discussion about a very stupid problem.

Perhaps they could print out this thread and bring it in to back up their work 😜

[u/spookyclever → u/Comprehensive-Ease10]

Yeah, this is a question I would have gotten confused over because I knew probability before I was good at getting percentages, which would have left high school me in this conundrum of “what’s wrong with the coin”? - or “is this some kind of weird trick question?”

For those who say this doesn’t make sense: I played a lot of Dungeons and Dragons, so I read up on probability, but “hated math” because my teachers never taught the application of the math until I got to geometry.

[u/kdaviper → u/Comprehensive-Ease10]

The probability of a fair coin landing on one side 63 times out of 90 is~.000056

[u/Ancient-Tomato1153 → u/kdaviper]

Fun fact, the probability of getting 63 or more of one side is .000094. (1 in 17,988 + 1 in 26,119), which is surprising, but certainly not impossible!

[u/randomlurker124 → u/Comprehensive-Ease10]

If I flipped a coin 90 times and the results were that skewed, I would almost certainly and reasonably assume the coin is uneven. 90 flips is not a small sample size and more than sufficient to demonstrate statistical significance. This would absolutely pass phase 1 medical trials for example, if the question was whether a drug worked. 

[u/MrInCog_ → u/Comprehensive-Ease10]

To be fair I’d still take some points off for not writing it in percent as the only unambiguous part of the task states, better yet not even in simplified form of 7/10.

[u/Dragon124515 → u/MrInCog_]

I mean, the kid knows that, OP directly states "I won't tell him what 63/90 is as a percent as a matter of principle against a poorly worded question" on their original post.

The kid came to the parent for help and they are refusing.

[u/tichris15 → u/Comprehensive-Ease10]

You can't reasonably assume a fair coin w/o a problem saying so in a math problem.

63/90 happens to be 70%...

[u/grundleHugs → u/Comprehensive-Ease10]

This question is to get the student to think about the hot hands fallacy of statistics. The previous result does not affect the outcome. It doesn't matter that the coin seems to come up heads more. The chance is still 50%

[u/Reasonable_Humor_738 → u/grundleHugs]

They just learned theoretical and experimental probability. Theorectically it is 50% and with this data it is 70% for experimental.

Look up the coin flip study. It is 51% for the side that is facing up.

There is nothing that says the coin is balanced and people cannot flip a coin perfectly everytime.

Why would a 7th math class teach the hot hands fallacy? This is when they start experiments in science and usually school coordinate so certain class lessons line up around others. This doesnt say fair coin. I get why you think it has to do with the hot hand fallacy but this is math and has nothing to do with emotion or psychology. There is no streak of success it is just data gathering. What bias do they have for the coin to flip certain ways?

[u/mekwall → u/gailonmiles]

70% is the experimental probability based on the 90 flips.

The theoretical probability for a fair coin is 50%.

The problem clearly intends 70%, otherwise the 90 flips and their results would be irrelevant.

But it should explicitly ask: "What is the experimental probability of landing on heads based on Sofia's results?"

That's an important distinction in probability theory, especially when teaching children.

[u/Hatta00 → u/mekwall]

Irrelevant information is part of a good math question. Math is how we understand the real world, and the real world is full of irrelevant information. Knowing what to ignore is a skill that needs to be tested.

[u/Any_Flan_6776 → u/gailonmiles]

They should write both answers as theoretical and experimental solutions

[u/redditydothis → u/gailonmiles]

Regression to the mean is a thing. 90 flips should be very close to 50/50. The coin must be altered or something.

[u/highgo1]

The question could benefit from having, "using these numbers" or something. Also, by 7th grade, studs should be able to reduce this fraction to 7/10. And then answer 70% for heads.

[u/realbobenray]

"Sofia flipped a coin 1 time and it landed on heads 1 time and tails 0 times. What is the probability of landing on HEADS?"

[u/kdizzle619]

This thread reveals how many people took statistics and its clear not many

[u/Sidoen → u/kdizzle619]

Look at the names, they're mostly GenAI bots I think.

And look at what they're saying, it's all worded to drive you nuts, make you comment to point out the flaws in their reasoning.

Dead internet right there!

[u/Sonamdrukpa → u/kdizzle619]

To be fair the first thing anyone who's taken statistics is going to say about this problem is that it's a badly written problem

[u/WomanInTheWood]

That depends on if your child is named Rosencrantz or Guildenstern. If so, 100% heads.

[u/Administrative_Bed5]

It doesn't say what kind of coin. If the teacher gave proper direction for the question, which is seems like they did based on the child's reaction, then you are causing problems by not allowing them to answer it properly.

[u/DesiccatedDesertRat]

Okay, I'm going to mildly infurate everyone using statistics.

You base probability or expected value on a coin is .5 or 50%, 45/90 (a binomial distribution).
Your observation is 63/90 or .7

The standard deviation for a binomial distribution across 90 coin flips is the square root of the number of flips multiplied by the probability of heads multiplied by the the probability of tails.

sqrt( 90 * .5 * .5 ) = 4.74 heads

Now you can calculate your z-score: Your observation subtracted by the expected value all divided by the standard deviation

(63-45)/4.74 = 3.79

Now if we look at a Z-Score of 3.79 (highly unlikely) on a standard normal distribution, you get a P-Value of 0.000074, or about a 1-in-13,500 chance of flipping heads on a fair coin 63 out of 90 times.

You can confidently assume that this coin is indeed biased.

How confident? Let me introduce you to Confidence Intervals!

Because the distribution is binomial and the distinction between heads vs tails is an arbitrary designation we shall use a 2 tailed P-value (the probability that it could be heads or tails 63/90 times). We simply take our original P-Value and multiply by two.
p=.00015 or .015%

Now for our CI equation! In this example we will be using an a value of a=.01 for 99% certainty (a Z-Score of 2.576)

Margin of Error = Sample Proportion +/- our Z-Score for 99% confidence multiplied by the square root of our observed percent of heads multiplied by the observed percent of tails divided by the number of flips

Margin of Error = .2576 * sqrt [ ( .7 *.3) / 90 ] = .124

Our Lower Bound = .7 - .124 = .576
Our Upper Bound = .7 + .124 = .824

A baseline fair coin should have a value of .5 which is outside the range of [.576, .824] so we can say with 99% certainty this is in fact a biased coin.

Now that we know that this is in fact a biased coin, we can ask our original question:
What is the probability of landing on heads?

Method 1: Point Estimate

p hat = Number of heads/Number of Flips
63/90 = .7 or 70%

Method 2: Interval Estimate

As illustrated above, with 99% confidence, the probability of flipping heads is somewhere between 57.6% and 82.4%
And even at a 95% confidence level (a=.05, z-score = 1.96) the probability of flipping heads is somwhere between 60.5% and 79.5%

I hope you have all found my explanation mildly infuriating

[u/glizzyMaster108 → u/DesiccatedDesertRat]

Man 7th grade math is not what i remember it like

[u/DarkShadowZangoose → u/DesiccatedDesertRat]

no no, your explanation is good

the probability of a fair coin flip is simply 50%, even with results like this

it doesn't say the coin is fair, but it doesn't say it's unfair either

however, 63/90 doesn't automatically assume a 70% probability and as you've calculated, the probability could indeed be 60-80%

70% is the percentage of flips that were heads in this test.

[u/AmbivalentFanatic]

The question is perfectly clear, you're just being given more info than you need. Your own critical thinking skills are at fault here, not the teacher.

[u/Opus_723]

Good lord, all these pedants busting out college-level stats theory to argue with the specific wording of a middle school math problem.

The kid is smarter than all of you because he recognizes that this is just a vapid prompt to get him to turn 63/90 into a percentage.

[u/Flat-Structure-7472]

As a teacher myself you need to work on your wording. "Write your answer as a PERCENT." is good. The other sentence should have been "What is the usual chance of a coin landing on either head or tails?".

[u/derpandderpette → u/Flat-Structure-7472]

Teacher hijacking the top comment to explain what is going on here. The students are learning about experimental vs theoretical probability. Theoretically it should be 50/100, but experimentally they got 63/90. I would bet dollars to doughnuts if we could see the rest of the worksheet it would say something about experimental probability somewhere on it.

Additionally, they are teaching how to convert fractions into decimals then into percentages. The students, likely using a calculator, are supposed to divide 63/90 to get 0.7. Then they are supposed to move the decimal place over two places to get 70%.

It’s actually annoying to see so many people here slamming the teacher and the problem when they have no idea this is a standard grade 4-6 outcome depending where you come from.

[u/exptimesea314]

I teach probability. This question is non-sense and shows complete incompetence about probability from the teacher. The only correct answer is that it is not possible to answer the question with full confidence, since the observation is compatible with any probability. The whole concept that mathematics is about interpretation of intention from a teacher is exactly why our kids grow up with a complete fear of mathematics. Fire the teacher.

[u/Creepslend → u/exptimesea314]

Wdym, it seems like a great trap set for students to see if they understand that the previous flips have nothing to do with the next one?

[u/lad_astro → u/Creepslend]

If it's that, then it must specify the coin is fair

[u/FormalWare]

Your seventh grader is a clever Bayesian.

[u/throwed101]

70% it doesn’t say if you flip the coin again. In this context it is asking what was the probability of the results.
I could see the wording being confusing,

[u/Beneficial-Band2604]

These questions are to help train people how to read and think critically. These were my favorite questions as a student because on homework where we shared our answers, I could see how many people simply didn't take time to read and understand the assignment.

It's a valuable skill, one that assists me to this day.

[u/Carbon-Base → u/Beneficial-Band2604]

Teaching kids critical thinking skills and common sense is immensely helpful and allows them to solve problems not just in math class, but in other classes and in life overall.

[u/swooptheowl22]

As someone with a bachelor's degree in statistics, this is such a bad question. They aren't learning about the law of large numbers in 7th grade (assuming this is a fair coin which isn't even mentioned).

We really need to raise the standards for teachers. I once got told I was doing algebra wrong in 5th grade and my parents had to get involved (both have PhDs in science).

[u/Knightrealmic → u/swooptheowl22]

I remember in fifth grade we were learning about calculating area based on more complex aggregate shapes. I asked about any arbitrary shape if we can approximate it by taking tons of smaller and smaller squares and she said that doesn’t work lol, it won’t ever get the right answer. That was something like twenty years ago

[u/KittyInspector3217 → u/Knightrealmic]

That confirms it, the moon landing was definitely fake. I knew calculus was bullshit!

[u/No_Interaction_5206 → u/Knightrealmic]

I figured out eulers polyhedron formula without being taught it and the teacher gave us no homework. It’s not the central limit theorem but still I’m guessing she was a bit smarter than your teacher lol.

I had another teacher who maintained that a profile of a roof is well described by a single right angle triangle. Mr Nelson if your reading this 20 years later your a damn idiot.

[u/Atomicnes → u/Knightrealmic]

Funny thing is you said the approximate answer which you could find by doing that

[u/hedoeswhathewants → u/Atomicnes]

What they described is one of the principles of calculus

[u/LackWooden392 → u/swooptheowl22]

Idk bro they taught me the law of large numbers in 7rh grade. They didnt call it that until 9th grade, but they did teach us that more iterations = more certainty

[u/Djolumn]

When similar questions are asked in statistics classes they often refer to the coin as a "fair coin".

[u/Gizogin]

I’d interpret this question not as “what is the probability that the next flip will land heads”. There’s no mention of a “next flip” anywhere, and the question does not provide enough information to make that determination.

It’s “what is the probability that a random coin flip chosen from this particular sample landed on heads”, which is 63/90, or 70%.

[u/Accomplished_Ice5073]

Z Score = ([Actual number of heads] less [expected number of heads]) divided by the square root of ([Number of flips] divided by 4)

Z = (63 - 45) / sqrt(90/4) = 3.79

In order for the coin to produce 63 heads on 90 flips, it would have to fall outside of 3.79 standard deviations from the norm. This translates in a z-score table to a probability of 0.0075%. This is about a 1 in 13,333 phenomenon.

So there is approximately a 1 in 13,333 chance the correct answer is 50%, the coin was perfectly balanced and it just happened to land on heads that many times, and approximately a 13,332 in 13,333 the coin in not balanced and therefore our only information of the coin's bias is the 90 flip sample, therefore the best answer is 70% (63/90).

[u/33rpm_neutron_star → u/Accomplished_Ice5073]

A P VALUE IS NOT THE PROBABILITY THAT THE NULL IS TRUE

cough Sorry, just had to get that off my chest. Your claim about the chances of it being fair is incorrect and misworded. Overall I agree with your take though.

Also, the problem should ask for your “estimate” of the probability of heads (they’re not learning about hypothesis testing).

[u/beene282 → u/Accomplished_Ice5073]

The fact that something happening by chance is 1 in 13,333 doesn’t mean there is a 13,332 in 13,333 chance it happened by design GIVEN it has happened.

The chance of me winning the lottery is 1 in 10 million, but if I show up tomorrow with a fortune, you can’t say there’s only a 1 in 10 million chance I won the lottery therefore there is a 9,999,999 in 10 million chance I got the money some other way.

[u/dvrichthofen]

These comments are amusing to read, but I think the real answer, as a highly involved parent, is that the school system is full of teachers that are barely educated themselves. I frequently encounter homework questions that either make no sense or have multiple correct answers and you're expected to guess which one the teacher expects.

Tl;dr never expect that the homework is correct, never assume that there is a correct answer.

[u/Longjumping_Wolf_912 → u/dvrichthofen]

A teacher didn’t write this question.

[u/RoastedPickledGoose → u/dvrichthofen]

Teacher checking in:

It’s very possible that is just a math worksheet from the company that made their textbooks. The teacher’s error is not checking those before giving them out.

In my school I have to give “common assessments” with others who teach the same subject. So we all give tests based on the test bank provided by the textbook maker. That way we’re all drawing from the same bank and the tests are (more or less) the same.

I’ve caught a bunch of instances where the test bank marked a (very clearly) wrong answer correct, and the correct answer as wrong. Every time I give a test, I double check every single question to make sure it is marked correctly before I give the test.

Point is, the teacher probably didn’t make that problem, they just didn’t bother to read it before giving out the worksheet.

[u/TatterhoodsGoat]

What is stopping him from calculating 63/90 as a percentage on his own? Does he not know what percentage means, not understand fractions, not know how to do division, or not understand how decimal places work? All of those seem important for carrying on with understanding probability.

[u/Starbike666]

The correct statistical answer to this question heavily depends on whether we assume 'the coin' is an officially minted coin, which is strongly presumed to be very, very close to fair, or if it could just be any random coin with heads and tail sides (and there are certainly ones that could include magic trick coins, weighted slugs, asymmetrical novelty tokens, etc).

The question does not say 'official' coin (or imply anything about uniformity or quality control or fairness). So, in an advanced class, I think it would probably be incorrect to assume that.

However, in a 7th-grade class, I would think that 'a coin' typically means an officially minted and circulated coin, which is assumed to be generally fair.

If you assume the coin was an 'official coin,' then you need to make one further assumption: is the flipping system itself biased? It is apparently possible to create a flipping system with this level of bias.

So, for the correct answer to be 50%*, you need to make two assumptions: that it is presumed to be an official coin with a strong presumption of being 'fair' and that the flipping system is also strongly presumed to be fair. If you don't make both those assumptions, then the answer is 70%**.

If you approach the question by assigning equal likelihood a priori to a fair or biased system/flipping, then after this flipping data, the probability that both fairness assumptions are true is approximately 0.5% (1/2 a percent). If you approached this question with a strong aprior presumption of fairness (e.g., an initial assumption of 90% that it is fair), then after the data, your posterior probability would be about 4% that it was fair. If you approach the question with the assumption that the likelihood is even over the entire range (0,1) then the probability of the system being fair is very small .0066%.

For a 7th grader, I would think the correct answer is 50%. For an advanced course, really, you would want to write an 'essay' about Bayesian priors, but I think ultimately the answer would be around 70% (or 69.6% using standard uninformative assumptions) because of the high likelihood of the system being biased based on the experimental data.

* More precisely, using US coins, apparently .508 depending on initial face orientation.

** More precisely 70% MLE, 69.75% Bayesian posterior predictive (0,1), 69.78% Jeffreys prior beta (.5,.5)

[u/Yusuf20904]

If the teacher marks 50% as wrong, your kid should ask them: if Sofia flipped then coin twice and came up heads both times, what would the probability of landing on heads be? If the teacher says 100%, they should be fired.

[u/Aggressive_Grade_732]

Okay, so this is kind of the meme curve where there's two jedi and one angry person in the middle.

Bottom: It's 63/90

Middle: NOOO IT'S A FAIR COIN SO IT'S ALWAYS 50%!

Top: Statistically speaking, if we do a binomial test, then given 90 flips, and 63 successes, the chance of getting 63 successes or greater is 0.0001. As a result, we can determine that undrr a p-value of 0.05, the coin is not, in fact, a fair coin, so the best estimate we have of the probability of flipping heads is the current mean, i.e. 63/90.

[u/Dangerous_Seaweed601]

It didn't say flipped a fair coin, either, though.. so..

[u/throwaway_76x]

People have already pointed out that the "known" results indicate this is a biased coin and since the question does not establish it as a fair coin, assuming the probability of heads as 50% would indeed be incorrect.

What I'm a bit more curious about is why is a seventh grader unable to convert 63/90 into a percentage without your help.

[u/Kheldar166 → u/throwaway_76x]

Probably because they were taught it a while ago and OP is more worried about getting internet points and owning their kids teacher than helping their kid with their maths

[u/Separate-Pickle9963]

Experimentally, 63 heads out of 90 trials is a small amount of evidentiary reason to suspect an unfair coin. If we assume the coin is fair as a given, the answer is 50%. If you flipped the coin 100,000 times, 63/90 would level out unless it was unfair, since it can take quite a while for stochastic data to level out.

[u/Integer_Domain]

I tutored a lot of primary ed majors in college. I would not want most of them teaching my child math.

[u/Frisky_Cow]

The real trouble with experimental probability, in action.

[u/beastmaster11]

This isnt a poorly worded question. It is intentionally a trick question. Now maybe your kids teacher explained that but just wanted it to be a division question and youre just not listening to your kid. Or maybe your kid misunderstood. Either way, this isnt the hill to die on

[u/TiltedLibra]

You know what the worksheet is asking, and by not helping your kid with the answer, the only person you are screwing is him.

[u/freegerator]

It doesn’t call it a fair coin