Question

$H$ is one of the $6$ horses entered for a race and is to be ridden by one of the two jokeys A and B. It is $2$ to $1$ that $A$ rides $H$ in which case all the horses are likely to win. If $B$ rides $H$, his chance is trebled. Then the odds against H winning is

• A. $4$ to $13$
• B. $13$ to $4$
• C. $13$ to $5$
• D. $13$ to $7$

Answer 1

Answer: (C)

$13$ to $5$

Probability of $H^{\prime }s$ winning
$=P$($A$ rides $H$ and $H$ wins)$+P$($B$ rides $H$ and $H$ wins)
$=\frac{2}{3}\times \frac{1}{6}+\frac{1}{3}\times \frac{3}{6}=\frac{5}{18}$
The required ratio is $\frac{13}{18}:\frac{5}{18}=13:5$