Question

For this problem, assume the box contains 9 red balls,
4 white balls, and 3 blue balls,
and that we choose two balls at random from the box.


What is the probability of neither being red
given that neither is white?

Answer 1

Let A be case where both balls are not red
Let B be case where both balls are not white
A and B is the case where neither is red nor is white, both are blue

P(A | B) = P(A and B)/P(B)

P(A) = 7/16 * 6/15 = 7/40
P(B) = 12/16 * 11/15 = 11/20
P(A and B) = 3/16 *2/15 = 1/40

--> P(A |B) = 1/40 * 20/11 = 1/22