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?
Age
14 to 16
Challenge level
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.