Question

If $x$ follows the Binomial distribution with parameters $n=6$ and $p$ and $9P(X=4)$ $=P(X=2)$ , then $p$ is

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

Answer 1

Answer: (A)

Given, 9P $(X=4)=P(X=2)$
$\therefore 9\cdot {}^6{C}_4{p}^4(1-p{)}^2={}^6{C}_2{p}^2(1-p{)}^4$
$\Rightarrow \frac{(1-p{)}^2}{p^2}=9$
$\Rightarrow \frac{1-p}{p}=3$
$\Rightarrow p=1/4$