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!**

## 1 comment:

There is another one you should "learn" or understand for your next Hedge Fund interview: Monty Hall problem

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