Class A contains 5 girls + 10 boys= 15 students. Class B contains 12 girls + 13 boys= 25 students. Teachers randomly pick a student from Class B and send them over to Class A; they then randomly pick a student from Class A. We're trying to find the probability that this student is a boy.
To answer this question, I calculated several conditional probabilities:
$P(F|A)=5/15$ $P(M|B)=13/25$ $P(F|B)=12/25$
What I tried next is the following, but I'm not sure this is the right way to go: P(M|A new)=(10+(13/25))/16=0.6575. Can you add the probability almost as a new student? If not, is there a simpler/more correct way to answer this question?