Finite math, Probability

Question

An unfair coin with Pr[H] = 0.65 is flipped. If the flip results in a head, one student is selected at random from a class of 4 girls and 6 boys. If the flip results in a tail, one student is selected from a different class containing 7 girls and 3 boys. find the probability that the flip resulted in a head given that a boy was selected?

Answer 1

Prob( Head | Boy) = Prob(Boy| head) Prob(Head)/ Prob(Boy)

Prob(Boy|head) = 0.65*0.6 = 0.39

Prob(Boy) = 0.65*0.6 + 0.35*0.3 = 0.495

0.39 * 0.65 / 0.495

= 0.512121212....