Question

$X$ follows a binomial distribution with parameters $n=6$ and $P$. If $4P(x=4)=P(x=2)$, then $P=$

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{6}$
• D. $\frac{1}{3}$

Answer 1

Answer: (D)

$\frac{1}{3}$

$4P(x=4)=P(x=2)$

$4{\times }^6{C}_4\times \left(P^4\right)\times (1-P{)}^2{=}^6{C}_2\times (P^2)\times (1-P{)}^4$

$4\times P^2=(1-P{)}^2$
$(3P-1)(P+1)=0$
$P=\frac{1}{3}$