Question

Before a race the chances of three runners, $A,B,C,$ were estimated to be proportional to $5,3,2$; but during the race $A$ meets with an accident which reduces his chance to one-third. What are now the respective chances of $B$ and $C?$

Answer 1

Before the race, A's chances of losing $=\frac{3}{10}\frac{2}{10}=\frac{1}{2}$

After the accident, A's chances of losing $=1-\frac{1}{3}=\frac{2}{3}$

$\therefore$ A's chances of lossing has increased in the ratio $\frac{4}{3}$

Hence, B's and C's chances of winning has also increased in the same ratio.

$\therefore$ B's new chances of winning $=\frac{3}{10}\times \frac{4}{3}=\frac{2}{5}$

and C's new chances of winning $=\frac{2}{10}\times \frac{4}{3}=\frac{4}{15}$