$14 \cdot 17$ In a mixed class of boys and girls, a student is selected to represent the class, with each student having an equal chance of being selected, and the probability of a boy being selected is $\frac{2}{3}$ of the probability of a girl being selected. Then the ratio of the number of boys to the total number of students in the class is
(A) $\frac{1}{3}$.
(B) $\frac{2}{5}$.
(C) $\frac{1}{2}$.
(D) $\frac{3}{5}$.
(E) $\frac{2}{3}$.
(36th American High School Mathematics Examination, 1985)
[Solution] Let the probabilities of a male and a female being selected be $p_{1}, p_{2}$, respectively. According to the problem, we have
$$
p_{1}=\frac{2}{3} p_{2} \text {, i.e., } 3 p_{1}=2 p_{2} \text {, }
$$

Therefore,
(Male students) : (Female students) $=2: 3$.

Thus, the proportion of male students in the entire class is $\frac{2}{5}$.
Hence, the answer is (B).