Question

The probability that a student get success in a competition is $\frac{3}{4}$. The probability that exactly $2$ out of $4$ students get success, is

• A. $\frac{9}{41}$
• B. $\frac{25}{128}$
• C. $\frac{1}{5}$
• D. $\frac{27}{128}$

Answer 1

Answer: (D)

$\frac{27}{128}$

Given, probability of success, $p=\frac{3}{4}$ and probability of failure, $q=1-p=\frac{1}{4}$
Here, total no. of students is $n=4$
Using binomial distribution,
Required probability $={}^n{C}_r\cdot p^{n-r}\cdot q^r$

$={}^4{C}_2{\left(\frac{3}{4}\right)}^2{\left(\frac{1}{4}\right)}^2$
$=\frac{4!}{2!2!}\times \frac{9}{16}\times \frac{1}{16}=\frac{27}{128}$