You have three bags, each containing two marbles. Bag #1 contains two white marbles, bag #2 contains two black marbles, and bag #3 contains one white marble and one black marble.
You pick a random bag and take out one marble. Given that this is a white marble, what is the probability that the remaining marble from the same bag is also white?
1 on 3 33%
ReplyDeleteits 50/50. the bag with 2 blacks is excluded
ReplyDeleteTwo to one in favor.
ReplyDeleteI think 2/3
ReplyDelete50-50. Only two bags have white marbles
ReplyDeleteI agree, 2/3:
ReplyDeleteYou essentially just start by picking a marble--and there are three white marbles. Two of those white marbles are in the same bag as another white marble; so, given that you've picked one of the three white marbles, 2/3 of the time its pair matches--right?
Correction to my entry #1
ReplyDeleteIt is 50/50, because only two bags are possible alternatives.
@ Anonymous:
ReplyDeleteBut if you've just picked a white marble, aren't you twice as likely to have drawn it from the bag with two whites? By my math, that still leaves a 2/3 chance of the marble's pair being white.
@oudeis:
ReplyDeletePast events have no influence on future probabilities at all.
Right now You have one white marble in your hand and knowledge, that another one is either black or white depending on which bag (out of two) you selected