Here is the question, and my solution (not at the interview though ;-))
We are given two drawers, one contains only black balls, the other one 50% black balls, and 50% white balls. I pick up a ball at random, it turns out that the ball is black, what is the probability that this black ball comes from the first drawer?
You must now remember the Bayes Theorem:
P(A|B) = P(B|A) * P(A) / P(B), where:
* P(A) is the prior probability of A
* P(A|B) is the conditional probability of A given B - or posterior probability
* P(B|A) is the conditional probability of B given A
* P(B) is the marginal probability of B
So, we can re-phrase the question like:
What is the probability that I picked up the first drawer (the one with only black balls), given that I picked up a black ball.
And we have:
* P(A) is the prior probability that I picked up drawer #1 without any other info, that is 1/2
* P(B) is the prior probability that I picked up a black ball without any other info, that is 3/4, because there are 1 black balls in #1, 0.5 black balls in #2, and 0.5 white balls in #2
* P(B|A) is the probability of getting a black ball given I chose drawer #1, because there are only black balls, it is 1
So we have P(A|B) = (1 * 1/2) / (3/4) = 2/3
So the answer is 2/3.
The good thing about this interview is that I will know the Bayes Theorem for the next one!