Question

Conditional Probability Assistance?

Answer 1

Let the event $A=\{ Sophomore \}, B=\{ Boy \}$

The the probability of the events

$P(A \cap B)=\frac{5}{12+18} =\frac{1}{6}$

$P( B)=\frac{12}{12+18} =\frac{2}{5}$

The conditional probability

$P(Sophomore|Boy)=P(A|B)=\frac{P(A \cap B)}{P(B)} =\frac{1/6}{2/5} =\frac{5}{12}$