Question

A man makes attempts to hit the target. The probability of hitting the target is $\frac{3}{5}$. Then the probability that $A$ hit the target exactly $2$ times in $5$ attempts is

• A. $\frac{144}{625}$
• B. $\frac{72}{3125}$
• C. $\frac{216}{625}$
• D. None of these

Answer 1

The correct option is A

$\frac{144}{625}$

Finding the probability:

Given,

$p=\frac{3}{4},q=\frac{2}{3},n=5,x=2$

By using binomial distribution,

The probability that a man hits the target exactly $2$ times in $5$ attempts is

$\begin{array}{rcl}& =& {}^{5}C_2\left(\frac{3}{5}\right)2\left(\frac{2}{5}\right)(5-2)\\ & =& {}^{5}C_2\left(\frac{3}{5}\right)2\left(\frac{2}{5}\right)3\\ & =& \frac{144}{625}\end{array}$

$\therefore$The required probability is $\frac{\mathbf{144}}{\mathbf{625}}$

Hence, the correct option is (A).