Question

One member of the debate team is going to be chosen President. Each member is equally likely to be chosen. The probability that a boy is chosen is 2/3 the probability that a girl is chosen. Girls make up what fraction of the debate team?

Answer 1

1/3

Answer 2

Solution:
Suppose there are B boys and G girls. Then
\[P(\text{boy chosen as President}) = \frac{b}{b+g},\]
and
\[P(\text{girl chosen as President}) = \frac{g}{b+g}.\] Hence
\[\frac{b}{b+g} = \frac23\left(\frac{g}{b+g}\right),\]
so b = (2/3)*g. This means that the ratio of boys to girls is 2:3, that is, for every 3 girls, there are 2 boys. Thus, for every 5 people on the team, 3 are girls and 2 are boys. Therefore girls make up 3/5 of the team.