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A is one of 5 horses that entered the race and for it to be rided by one of the two jokeys P & Q and odds in favour of P rides it is 2 to 1. If P rides A, all the horses are equally likely to win. If Q rides A, A's chance of winning is tripled. The odds in favour of A's winning is

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3 : 1

2 : 1

1 : 3

1 : 2

answer is C.

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Detailed Solution

$E_{1} =$ Jockey P rides

$E_{2} =$ Jockey Q rides

odds in favour of O is $P (E_{1}) : P (E_{1}) = 2 : 1$

$P (E_{1}) = \frac{2}{3} P (E_{2}) = \frac{1}{3}$

E=horse A wins

$\begin{array}{rcl} P (\frac{E}{E_{1}}) & = & \frac{1}{5} P (\frac{E}{E_{2}}) = \frac{3}{5} \\ P (E) & = & \frac{2}{3} \times \frac{1}{5} + \frac{1}{3} \times \frac{3}{5} = \frac{5}{15} = \frac{1}{3} \\ P (E) & = & \frac{2}{3} \end{array}$

odds in favour $P (E) : P (E) = 1 : 2$

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