There are 8 boys and 6 girls in a class. If two students are selected at random from the class, find the probability that they are of
(a) the same sex ;
(b) different sex.
Explanation
(p(boys) = frac{8}{14} = frac{4}{7})
(p(girls) = frac{6}{14} = frac{3}{7})
(a) p(both are of the same sex) = p(both are boys or both are girls)
= (frac{8}{14} times frac{7}{13} + frac{6}{14} times frac{5}{13})
= (frac{86}{182})
= (frac{43}{91})
(b) p(they are of different sex) = p(first is a boy and second is a girl or first is a girl and second is a boy)
= (frac{8}{14} times frac{6}{13} + frac{6}{14} times frac{8}{13})
= (frac{96}{182})
= (frac{48}{91})