Question

Suppose $X$ follows a binomial distribution with parameters $n=6$ and $p$. If $9P(X=4)=P(X=2)$, find $4p$

Answer 1

$9P(X=4)=P(X=2)$
$\Rightarrow 9{\cdot }^6{C}_4{p}^4{q}^2{=}^6{C}_2{p}^2{q}^4[q=1-p]$
$\Rightarrow 9p^2=q^2\left[{\because }^6{C}_4{=}^6{C}_2\right]$
$\Rightarrow 3p=q=1-p[\because q>0]$
$\Rightarrow 4p=1$