Question

Three athletes $A,B$ and $C$ participate in a race competition.

The probability of winning $A$ and $B$ is twice of winning $C$,

Then the probability that the race win by $A$ or $B$ is

• A. $\frac{2}{3}$
• B. $\frac{3}{4}$
• C. $\frac{4}{5}$
• D. $\frac{1}{6}$

Answer 1

The correct option is C

$\frac{4}{5}$

Explanation of the correct option.

Let's assume $P\left(A\right)$ is the probability of winning race by $A$, $P\left(B\right)$ is the probability of winning race by $B$ and $P\left(C\right)$ is the probability of winning race by $C$.

Given : $P\left(A\right)=P\left(B\right)=2P\left(C\right)$

We know that, $2P\left(C\right)+2P\left(C\right)+P\left(C\right)=1$

$\Rightarrow$$P\left(C\right)=\frac{1}{5}$

Therefore, $P\left(A\right)=P\left(B\right)=\frac{2}{5}$.

Thus the probability that the race win by $A$ or $B$ is given by $P\left(A\right)+P\left(B\right)$

$\begin{array}{rcl}P\left(A\right)+P\left(B\right)& =& \frac{2}{5}+\frac{2}{5}\\ & =& \frac{4}{5}\end{array}$

Therefore the probability that the race win by $A$ or $B$ is $\frac{4}{5}$.

Hence, option (C) is the correct option, i.e. $\frac{4}{5}$.