# Two Girls

There are 10 girls in a mixed class. If two pupils are selected, the probability that they are both girls is 0.15. How many boys are in the class?

## Problem

There are $10$ girls in a mixed class.

If two pupils from the class are selected at random, then the probability that both are girls is $0.15$

How many boys are in the class?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

## Student Solutions

**Let the number of boys in the class be $x$.**

Hence $\frac{10}{10+x}\times\frac{9}{9+x} = 0.15 = \frac{3}{20}$.

Simplifying gives $1800=3(10+x)(9+x)$ and then $x^{2}+19x-510=0$.

Factorising gives $(x+34)(x-15)=0$ and, since $x\not=-34$, $x=15$.

**Alternatively, let the number of students in the class be $x$.**

Hence $\frac{10}{x}\times\frac{9}{x-1} = 0.15 = \frac{3}{20}$.

Simplifying gives $600=x(x-1)$ and then $x^{2}-x-600=0$.

Factorising gives $(x+24)(x-25)=0$ and, since $x\not=-24$, $x=25$.

Therefore the number of boys in the class is 15.

*Students from Comberton Village College sent us these solutions.*