Let the event [tex] A=\{ Sophomore \}, B=\{ Boy \} [/tex]
The the probability of the events
[tex] P(A \cap B)=\frac{5}{12+18} =\frac{1}{6} [/tex]
[tex] P( B)=\frac{12}{12+18} =\frac{2}{5} [/tex]
The conditional probability
[tex] P(Sophomore|Boy)=P(A|B)=\frac{P(A \cap B)}{P(B)} =\frac{1/6}{2/5}
=\frac{5}{12} [/tex]
