Question

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

• A. $\frac{5}{13}$
• B. $\frac{18}{5}$
• C. $\frac{13}{18}$
• D. $\frac{13}{5}$

Answer 1

The correct option is D $\frac{13}{5}$

When $B$ rides $A$ probability of winning of
$A=\frac{2}{3}\times \frac{1}{6}$
When $C$ rides $A$ probability of winning of
$A=\frac{1}{3}\times \frac{1}{6}\times 3$
$\therefore P\left(A\right)=\frac{2}{18}+\frac{1}{6}=\frac{5}{18}$
Now odds against his winning $=\frac{18-5}{5}=\frac{13}{5}$