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Follow up question: > You are given an urn containing 100 balls; n of them are red, and 100-n are green, where n is chosen uniformly at random in [0, 100]. You
by orlp 3y ago
Follow up question:
> You are given an urn containing 100 balls; n of them are red, and 100-n are green, where n is chosen uniformly at random in [0, 100]. You select 99 balls at random and find that they are all red. What is the probability the last ball is red?
- russdill 3y ago50%. With current knowledge N is either 100 or 99 with an equal probability.
- a_cardboard_box 3y agoInitially there is an equal chance that there are 99 or 100 red balls. But if there is a green ball, it is unlikely to be the last picked. So the fact that you saw 99 red balls makes it unlikely there is a green ball.
- addandsubtract 3y agoNo, the chance of it being red is much higher. If there's one green ball in the jar, than all previous draws would've needed to avoid the green one. The chances of that happening are way less than 50%.
- deleted 3y ago[deleted]
- fallingsprings 3y agoThis is a fantastic follow up question. The last ball is overwhelmingly likely to be red, though this is very counterintuitive. The “all-red” urn and the “all-red-but-one” urn were equally likely to be chosen at the start. But the draws have given you a lot of info about which distribution you’ve been drawing from. Were you sampling from the all-red distribution, your draws would be totally unsurprising — you would observe a run of 99 consecutive reds 100% of the time. If you were you sampling from the all-red-but-one distribution, however, you’d only have observed this outcome 1/100 times.