1985 AHSME Problem 6

One student in a class of boys and girls is chosen to represent the class. Each student is equally likely to be chosen and the probability that a boy is chosen is \frac{2}{3} of the probability that a girl is chosen. The ratio of the number of boys to the total number of boys and girls is

\mathrm{(A)\ } \frac{1}{3} \qquad \mathrm{(B) \ }\frac{2}{5} \qquad \mathrm{(C) \ } \frac{1}{2} \qquad \mathrm{(D) \ } \frac{3}{5} \qquad \mathrm{(E) \ }\frac{2}{3}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.