1985 AMC 12 Problem 6

Question

One student in a class of boys and girls is to be chosen to represent the class. Each student is equally likely to be chosen and the probability that a boy is chosen is

\frac23

of the probability that a girl is chosen. The ratio of the number of boys to the total number of boys and girls is

\frac13

\frac25

\frac12

\frac35

\frac23

Answer: B

Concepts:basic probability ratio and proportion

Difficulty rating: 1100

Small hint:

Equal likelihood makes the selection probabilities proportional to the class counts

Big hint:

A boys-to-girls ratio of

2:3

uses five equal parts in all

Solution:

Because every student is equally likely to be selected, the number of boys is

\frac{2}{3}

of the number of girls. Thus the boys-to-girls ratio is

2:3,

and boys make up

\frac{2}{2+3}=\frac{2}{5}

of the class.

Thus the correct answer is B.