Question

Mean and variance of binomial variable X are 2 and 1 respectively, then $P(X\ge 1)$ is

• A. $\frac{2}{3}$
• B. $\frac{7}{8}$
• C. $\frac{4}{5}$
• D. $\frac{15}{16}$

Answer 1

The correct option is D $\frac{15}{16}$

Here, $np=2,npq=1$
$\therefore p=q=\frac{1}{2},n=4$
$\therefore P(X\ge 1)=1-P(X=0)=1{-}^4{C}_0{\left(\frac{1}{2}\right)}^4=1-\frac{1}{16}=\frac{15}{16}$