2.2.3 problem 36

(a)

Since any applicant who is good at baseball is accepted to the college, the proportion of admitted students good at baseball is higher than the proportion of applicants good at baseball, because applicants include people who aren’t good at either math or baseball.

(b)

Let $S$ denote the sample space. Then,

$P\left(A\right|B,C)=P(A\left|B\right)=P\left(A\right)=P\left(A\right|S)<P(A\left|C\right)$.