I always find this use of "statically the result is" to be kind of misleading. 11.25 is the expected value or the mean result across very large sampling with the results following a normal distribution. In this case the probability of getting 11 right on 45 guesses is C(45,11) * 0.7534 * 0.2511 ≈ 0.1367. Even if we include the probability of getting 12 which is ≈ 0.1291, the combined probability of getting 11 or 12 is 26.6%. Which is to also say, the probability of not getting 11 or 12 is 73.4%. "Statistically" they are nearly 3 times as likely to not get 11 or 12 than get 11 or 12. See how using the mean as the "statistical" result is misleading and meaningless?
My professor always said the expected value of a dice roll is 3.5, but you will never roll a 3.5. In fact you are just as likely to roll a 1, 2, 3, 4, 5, or 6.
am i trippin balls, how does this have any upvotes? they are rolling a separate chance for every question, it’s SO much different from rolling a die once. if you roll one 6-sided die once, it’s probably not going to be 3 or 4. if you roll it 45 times, the result probably adds up to something around 157.5 - which, by the way, is what standard deviation means.
this is going to cluster to form a bell curve not too dissimilar to a normal distribution. you seem to focus a lot on the individual probability of 11, but the probability of getting 9-13 questions right is 61%. the probability of getting only one or all 45 is basically zero. it’s obviously not equal despite the fact you made it look like it on the dice example (for some reason???). obviously it’s not going to be a score of exactly 11.25 (that doesn’t even make sense even ignoring the fact that we started at question 20, not 1). but it’s probably going to be around those values.
(OF COURSE, there are far too many unknowns here. what did this person answer up til question 20? are there only 4 choices or more? do points get docked for wrong answers?)
If you allow "Statistically he'll get an 11.25" to be a correct statement, which really means the expected value is 11.25, then the statement "Statistically a dice roll results in 3.5" is also correct because it is also saying the expected value is 3.5. The dice roll analogy is to illustrate saying "Statistically the result is the expect value" is absurd and misleading.
Here's another example. In 2024 the traffic fatality rate in the US is 1.19 fatalities per 100 million miles traveled. So if John drives a hundred miles per week for commute, could you say "Statistically John died 0.00000119 times per week"? That is the statement "Statistically the result is the expected value."
Just so you know, while the 11.25 average on 45 questions approximates a normal distribution (it is NOT a normal distribution, just approximates one), a single dice roll absolutely does not follow the same rule. A single dice roll has equal probability for every roll. You are still working with false equivalence and a terrible understanding of statistics.
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u/captain_salt_bag 20h ago
Statistically he'll get an 11.25 lol
(25%)