## Wednesday, January 25, 2012

### 3 Bags of Marbles

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. 1 on 3 33%

2. its 50/50. the bag with 2 blacks is excluded

3. Two to one in favor.

4. I think 2/3

5. 50-50. Only two bags have white marbles

6. I agree, 2/3:

You 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?

7. Correction to my entry #1

It is 50/50, because only two bags are possible alternatives.

8. @ Anonymous:
But 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.

9. @oudeis:
Past 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

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