Question

If r.v. $X\sim B(n=5,P=\frac{1}{3})$, then $P(2<X<4)=$...........

• A. $\frac{80}{243}$
• B. $\frac{40}{243}$
• C. $\frac{40}{343}$
• D. $\frac{80}{343}$

Answer 1

The correct option is B $\frac{40}{243}$

As $X$ can take only integer values, so $P(2<X<4)=P\left(3\right)$.

Also, let $Q=1-P=\frac{2}{3}$

we have,

$P\left(3\right)=$ ${}^5{C}_3.{\left(\frac{1}{3}\right)}^3.{\left(\frac{2}{3}\right)}^2$ ...... Using binomial distribution

$=\frac{40}{243}$

answer (b).