Question

There are $7$ horses in a race, Mr $\mathrm{X}$ selected $2$ horses at random and bet on them. The probability that Mr $\mathrm{X}$ selected the winning horse is

• A. $\frac{1}{7}$
• B. $\frac{4}{7}$
• C. $\frac{3}{7}$
• D. $\frac{2}{7}$

Answer 1

The correct option is D

$\frac{2}{7}$

Find the required probability

Given, there are total number of $7$ horses.

Thus, the probability $\mathrm{P}\left(\mathrm{w}\right)$ that Mr. $\mathrm{X}$ selects the winning horse is

$\Rightarrow$$\begin{array}{rcl}\mathrm{P}\left(\mathrm{w}\right)& =& \frac{({}^1\mathrm{C}_1\mathrm{x}{}^6\mathrm{C}_1)}{{}^7\mathrm{C}_2}\end{array}$ $\mathbf{.}\mathbf{.}\mathbf{.}\left[{}^{n}C_r=\frac{n!}{r!\times (n-r)!}\right]$

$\begin{array}{rcl}& \Rightarrow & \mathrm{P}\left(\mathrm{w}\right)=\frac{6}{21}\\ & \Rightarrow & \mathrm{P}\left(\mathrm{w}\right)=\frac{2}{7}\end{array}$

Hence option $\left(\mathrm{D}\right)$, $\frac{2}{7}$ is the correct answer.