Question

In a binomial distribution, the mean is $\frac{2}{3}$ and the variance is $\frac{5}{9}$. What is the probability that $X=2$?

• A. $\frac{5}{36}$
• B. $\frac{25}{36}$
• C. $\frac{25}{216}$
• D. $\frac{25}{54}$

Answer 1

Answer: (C)

$\frac{25}{216}$

We have $\mu =np=\frac{2}{3}$ and ${\sigma }^2=np(1-p)=\frac{5}{9}$.

This give $p=\frac{1}{6}$ and $n=4$.

Also, $P(X=r){=}^n{C}_r{p}^r(1-p{)}^{n-r}⟹P(X=2){=}^4{C}_2{\left(\frac{1}{6}\right)}^2{\left(\frac{5}{6}\right)}^2=\frac{25}{216}$