bernoulli problem

Question

An unfair coin with Pr[H]=0.28 is flipped. If the flip results in heads, a student is selected at random from a class of 10 boys and 7 girls. Otherwise, a student from a different class containing 11 boys and 7 girls is selected.
What is the probability of selecting a girl?

What is the probability of selecting a girl, given that the flip resulted in heads??

Answer 1

If the result of the flip was a heads, then probability of a girl is 0.28 * 7/17 ≈ 0.115

 

If the result of the flip was tails, the probability of a girl is 0.72 * 7/18 ≈ 0.28

 

P[Selecting a girl] ≈ 0.115 + .28 = 0.395

 

If the flip is known to have resulted in head, P[Selecting a girl] = 7/17 ≈ 0.412