Question

If $X$ is a binomial variate with $n=6$ and $9P(X=4)=P(X=2)$, the parameter $p$ is

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

Answer 1

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

$9P(X=4)=P(X=2)$
$9{}^6{C}_4{p}^4(1-p{)}^2={}^6{C}_2{p}^2(1-p{)}^4$
$9p^2=(1-p{)}^2$
$3p=(1-p)$
$4p=1$
$p=\frac{1}{4}$