Question

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

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

Answer: (A)

$\frac{1}{2}$

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