Question

In a binomial distribution, the sum of its mean and variance is $1.8$. Find the probability of two successes, if the event was conducted $5$ times.

• A. $0.2623$
• B. $0.2048$
• C. $0.302$
• D. $0.305$

Answer 1

Answer: (B)

Here $np+npq=1.8$ and $n=5$
$\Rightarrow 5p\left(1+q\right)=1.8$
$\Rightarrow \left(1-q\right)\left(1+q\right)=0.36$
$\Rightarrow 1-q^2=0.36$
$\Rightarrow q^2=0.64$
$\Rightarrow q=0.8$ (Taking + ve value only)
$\therefore n=5$, $p=0.2$, $g=0.8$
$\therefore$ Probability of $2$ successes $=P\left(2\right)={}^5{C}_2{p}^2{q}^3$
$=10{\left(0.2\right)}^2{\left(0.8\right)}^3=0.2048$