Question 12

In a given race the odds in favour of three horses A, B, C are 1:3; 1:4; 1:5 respectively. Assuming that dead heat is impossible the probability that one of them wins is

Solution

Odds in favour of A = 1:3, thus P(A wins) = $$\frac{1}{1+3}=\frac{1}{4}$$

Odds in favour of B= 1:4, thus P(A wins) = $$\frac{1}{1+4}=\frac{1}{5}$$

Odds in favour of C = 1:5, thus P(A wins) = $$\frac{1}{1+5}=\frac{1}{6}$$

Since deadheat is not possible only 1 will win.

P(A or B or C wins) = $$\frac{1}{4}+\frac{1}{5}+\frac{1}{6}=\frac{37}{60}$$

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