Question

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

• A. $\frac { 28 } { 256 }$
• B. $\frac { 219 } { 256 }$
• C. $\frac { 128 } { 256 }$
• D. $\frac { 37 } { 256 }$

Answer 1

Answer: (A)

$\frac { 28 } { 256 }$

Answer 2

$\left. \begin{array} { c } n p = 4 \\ n p q = 2 \end{array} \right\}$

⇒$q = \frac { 1 } { 2 } , p = \frac { 1 } { 2 } , n = 8$

$p ( X = 2 ) = { } ^ { 8 } C _ { 2 } \left( \frac { 1 } { 2 } \right) ^ { 2 } \left( \frac { 1 } { 2 } \right) ^ { 6 } = 28 \cdot \frac { 1 } { 2 ^ { 8 } } = \frac { 28 } { 256 }$.