Question

Suppose $X$ is a binomial variate $B(5,p)$ and $P(X=2)=P(X=3)$, then $p$ is equal to

• A. $1/2$
• B. $1/3$
• C. $1/4$
• D. $1/5$

Answer 1

The correct option is A $1/2$

Here $N=5$
Given $P(X=2)=P(X=3)$
${\Rightarrow }^5{C}_2{p}^2(1-p{)}^3{=}^5{C}_3{p}^3(1-p{)}^2$
$\Rightarrow 1-p=p\therefore p=\frac{1}{2}$