Question

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

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

Answer 1

The correct option is A $\frac{1}{4}$

Given, $9P(X=4)=P(X=2)$

$\therefore 9{}^6{C}_4{p}^4(1-p{)}^2={}^6{C}_2{p}^2(1-p{)}^4$

$\Rightarrow \frac{(1-p{)}^2}{p^2}=9$ ............ $\because {}^6{C}_2{=}^6{C}_4$

$\Rightarrow \frac{1-p}{p}=3$

$\Rightarrow p=\frac{1}{4}$