Question

A class in advanced physics is composed of 10 juniors, 30 seniors, and 10 graduate students. The final grades show that 3 of the juniors, 10 of the seniors, and 5 of the graduate students received an A for the course. If a student is chosen at random from this class and is found to have earned an A , what is the probability that he or she is a senior?

Answer 1

P(S/A)= P(S,A)/P(A)

P(A)=(3+10+5)/(10+30+10)=18/50=9/25

P(S,A)=10/50=1/5

then P(S/A)=(1/5)/(9/25)=5/9=0.55