What is the probability of selecting 1 mouse of each gender given that both are grey?

Question

For this problem, assume there are 5 grey females, 2 grey males, 4 white females, and 5 white males. As in the book, the biologist selects two mice randomly.

(1) What is the probability of selecting two males given that both are grey?

(2) What is the probability of selecting 1 mouse of each gender given that both are grey?

Answer 1

1) 2/(2+5) = 2/7 x 1/6 = 2/42 = 1/21

2) 5/7 x 2/6 = 5/7x1/3 = 5/21 x 2= 10/21

chance of 2 females = 5/7x4/6 =20/42 = 10/21

10/21+ 10/21 +1/21 = 21/21 = 1