Question

A friend has two kittens (one brown and the other black) and is offering one to you. You only want a kitten if it is female. The friend asks her veterinarian if at least one of the kittens is female. The veterinarian replies, “Yes!” What is the probability that if you select the black kitten, it is a female? List all of the possible outcomes given that at least one of the cats is a female.

Answer 1

All possible outcomes that at least one of the cat is female: {(F, M), (M, F), (F, F)} where (X, Y) implies X is gender of brown kitten and Y is gender of black kitten.

$\tiny P(Female | Black)=\frac{P(Female \cap Black)}{P(Black)}=\frac{\frac{1}{3}}{\frac{2}{3}}=\frac{1}{2}$

Hence, 1/2 or 0.5 is the probability that if you select the black kitten it is female.