What's the probability of picking two boys?

A class of 27 students is split between boys and girls in the ratio of 5:4.
What's the probability of picking two boys?

-/|\-

Solution

The ratio is in nine parts, so each part is $\frac{27}{9}=3$ students.
Therefore the class has $5\times 3=15$ boys.
The probability the first student picks is a boy is $\frac{15}{27}$ and the second is $\frac{14}{26}$.

So the probability of two boys being picked, at random, is $$\frac{15}{27}\times \frac{14}{26}=\frac{35}{117}$$

-oOo-