Question

Let $X\sim B(n,p)$, if

$E\left(X\right)=5,Var\left(X\right)=2.5$, then $P(X<1)=$...................

• A. ${\left(\frac{1}{2}\right)}^{11}$
• B. ${\left(\frac{1}{2}\right)}^{10}$
• C. ${\left(\frac{1}{2}\right)}^6$
• D. ${\left(\frac{1}{2}\right)}^9$

Answer 1

The correct option is B ${\left(\frac{1}{2}\right)}^{10}$

$E\left(X\right)=npVar\left(X\right)=npq$

where $n=$ number of trials, $p=$ probability of a success, $q=$ probability of a failure

Given $E\left(X\right)=5$

$Var\left(X\right)=2.5$

$\Rightarrow n=10,p=\frac{1}{2},q=\frac{1}{2}$

$P(X<1)={\left(\frac{1}{2}\right)}^{10}$