Let the event [tex] A=\{ Freshman\}, B=\{ Boy \} [/tex]
The the probability of the events
[tex] P(A \cap B)=\frac{4}{12+18} =\frac{2}{15} [/tex]
[tex] P( B)=\frac{12}{12+18} =\frac{2}{5} [/tex]
The conditional probability
[tex] P(Freshman|Boy)=P(A|B)=\frac{P(A \cap B)}{P(B)} =\frac{2/15}{2/5} =\frac{1}{3} [/tex]
