Question

In a horse race, the odds in favor of three horses are $1:2,1:3,\mathrm{and}1:4$. The probability that one of the horses will win the race is.

• A. $\frac{7}{60}$
• B. $\frac{47}{60}$
• C. $\frac{1}{4}$
• D. $\frac{3}{4}$

Answer 1

The correct option is B

$\frac{47}{60}$

Explanation for the correct answer:

Find the probability.

Given, the odds in favor of three horses $A,B\mathrm{and}C$are $1:2,1:3,\mathrm{and}1:4$.

So if the odds in favor $=a:b$, then the probability $=\frac{a}{a+b}$

Thus,

The probability that the horse $A$ wins is $P\left(A\right)=\frac{1}{2+1}=\frac{1}{3}$

The probability that the horse $B$ wins is $P\left(B\right)=\frac{1}{3+1}=\frac{1}{4}$

The probability that the horse $C$ wins is $P\left(C\right)=\frac{1}{4+1}=\frac{1}{5}$

The probability that one of the horses will win the race is $P\left(A\right)+P\left(B\right)+P\left(C\right)=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}=\frac{47}{60}$.

Hence, the correct option is B.