Question

If the probability of a horse $A$ winning a race is $\frac{1}{4}$ and the probability of a horse $B$ winning the same race is $\frac{1}{5}$, then the probability that either of them will win the race is

• A. $\frac{1}{20}$
• B. $\frac{9}{20}$
• C. $\frac{11}{20}$
• D. $\frac{19}{20}$

Answer 1

The correct option is B

$\frac{9}{20}$

Step1: Solve for required probability,

Let $A$ be the event that horse $A$ wins and $B$ be the event that horse $B$ wins the race.

Given that, $P\left(A\right)=\frac{1}{4}$, and $P\left(B\right)=\frac{1}{5}$

The probability that either of them wins = $P\left(AUB\right)$

$P\left(AUB\right)=P\left(A\right)+P\left(B\right)–P(A\cap B)$

(As the event $A$ and $B$ are mutually exclusive,$P(A\cap B)=0)$

$P\left(AUB\right)=\frac{1}{4}+\frac{1}{5}$

$P\left(AUB\right)=\frac{9}{20}$

Hence, option B is correct.