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

One simple approach is to consider that there are 2 grey males (M1, M2) and 5 grey females (F1, F2, .. , F5).

 

If you form all grey couples with these 7 mice, the possibilities are

 

M1M2, M1F1, M1F2, M1F3, M1F4, M1F5, M2F1, M2F2, M2F3, M2F4, M2F5     i.e, 11 possible cases

 

The only case that fits your requirement (two males) is M1M2,                 i.e., 1 case

 

Thus the probability that both are males give that both are grey is 1/11.