Question

A bag contains five red balls and four yellow balls. If we select two balls at random, what is the probability that the second ball is red given that the first ball was red?

Assume sampling without replacement.

Answer 1

The probability is `1/2`.

Explanation:

First off, we know that there is a `5/9` chance that a red ball will be picked and that there is a `4/9` chance that a yellow ball will be picked. A red ball is picked out and not replaced. This is important because now there are 8 balls in the bag, not 9. There is now a `4/8`, or `1/2` chance that a red ball will be picked and a `1/2` chance that a yellow ball will be picked. Since the question asks for the probability of a red ball being picked, the probability is `1/2`.