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Change it to drawing from a normal distribution... the answer will change dramatically and get very close to what one would likely consider "common sense", ie t
by danielmarkbruce 3y ago
Change it to drawing from a normal distribution... the answer will change dramatically and get very close to what one would likely consider "common sense", ie that it remains close to 50/50. I think binomial gets it to 50/50.
Humans aren't wired for uniform distribution. 100 reds seems crazy unlikely compared to 50/50, yet this trick question makes those equally likely.
- j7ake 3y agoHow would normal distribution change the result? I am imaging a random number generated from truncated normal distribution with mean 50, clipped 0 and 100: the answer will still lean right. How would binomial work? You have 101 urns from which to choose.
- danielmarkbruce 3y agoNormal: it is very close to 50/50. It does still lean, but only just. It's close enough that in practice any guess is fine. Binomial: it is 50/50. The reason these change the situation dramatically is that under normal or binomial, you are waaaay more likely to be in a situation that is close to 50/50 to begin with because they are way more likely to occur. The quirk of this question is that a 0 green 100 red urn is just as likely as a 50-50 red/green urn using a uniform distribution - hence if you get red on the first draw you are much more likely to be in a heavily tilted red urn.
- j7ake 3y agoHow would binomial work here? You’re choosing amongst 101 urns of different proportions. How do you narrow 101 choices into two?