Question

If for a binomial distribution $n=4$ and $6P(X=4)=P(X=2)$, the probability of success is

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

Answer 1

The correct option is B $1/2$

If for a binomial distribution n=4
$6P(X=4)=P(X=2)P(X=k){=}^n{C}_k{p}^k(1-p{)}^{n-k}$

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

$6p^2=6{(1-p)}^2$
$1-2p=0$

$p=$ $\frac{1}{2}$