Question

In a given race, the odds in favour of horses $H_1,H_2,H_3$ and $H_4$ are 1:2, 1:3, 1:4, 1:5 respectively. Find the probability that one of them wins the race.

• A. $\frac{57}{60}$
• B. $\frac{1}{20}$
• C. $\frac{2}{7}$
• D. $\frac{7}{60}$

Answer 1

The correct option is A $\frac{57}{60}$

$P\left(H_1\right)=\frac{1}{3},P\left(H_2\right)=\frac{1}{4},P\left(H_3\right)=\frac{1}{5},P\left(H_4\right)=\frac{1}{6}\therefore P(H_1\cup H_2\cup H_3\cup H_4)=P\left(H_1\right)+P\left(H_2\right)+P\left(H_3\right)+P\left(H_4\right)=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}=\frac{57}{60}$