October 4, 2015

Continuing the Monty Hall problem, I need to mention there is another similar question: Bertrand's box paradox. If you know how to calculate the conditional probability, this kind of question is much easier. I have seen a similar one during my interview at SanDisk.

Question: There are 3 cars. One is completely black, and another one is completely white. The third one has one side black, and the other side white. Suppose you see one car has a black side, what is the probability that the other side is also black?

This a very standard conditional probability problem. We know:

This is very similar to the Bertrand's box paradox, where coins are drawn from 3 boxes.