NIMCET 2017 Question Paper with solutions

According to the questions, we have
Mean = np = 4 and variance = npq = 2
∴ 4p = 2
⇒ q = $\frac{1}{2}$
Now , p = 1 - q = 1 - $\frac{1}{2}$ = $\frac{1}{2}$
and np = 4
⇒ n × $\frac{1}{2}$ = 4
⇒ n = 8
∴ n = 8 , p = $\frac{1}{2}$ , q = $\frac{1}{2}$
Now, by binomial distribution, we know that
P (X = r) = $\stackrel{\mathit{n}}{}{\mathit{C}}_{\mathit{r}}{\mathit{p}}^{\mathit{r}}{\mathit{q}}^{\mathit{n}-\mathit{r}}$
∴ P (X = 1) = $\stackrel{8}{}{\mathit{C}}_1$ ${\left(\frac{1}{2}\right)}^1{\left(\frac{1}{2}\right)}^{8-1}$ = 8 × ${\left(\frac{1}{2}\right)}^8$ = $\frac{1}{32}$