Question

In a binomial distribution with $n=4$, if $2P(X=3)=3P(X=2)$, then value of p is?

• A. $\frac{9}{13}$
• B. $\frac{4}{13}$
• C. $\frac{6}{13}$
• D. $\frac{7}{13}$

Answer 1

The correct option is A $\frac{9}{13}$

$P(X=3)={}^4{C}_3{p}^3(1-p)=4p^3(1-p)$

$P(X=2)={}^4{C}_2{p}^2(1-p{)}^2=6p^2(1-p{)}^2$

$8p^3(1-p)=18p^2(1-p{)}^2$

$4p=9(1-p)$

$13p=9$

$p=\frac{9}{13}$