MCQ
Let $X \sim B(n, p)$, if $E(X)=5, \operatorname{Var}(X)=2.5$ 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$\left(\frac{1}{2}\right)^9$
(b): $\because E(X)=n p=5$ ...(i)
and $\operatorname{Var}(X)=n p q=2.5$ ...(ii)
From (i) and (ii), we get
$
\frac{n p q}{n p}=\frac{2.5}{5} \Rightarrow q=\frac{1}{2}
$
Since, $p+q=1 \Rightarrow q=1-\frac{1}{2}=\frac{1}{2}$
$\therefore n=\frac{5}{1} \times 2=10$ (From (i))
$\Rightarrow P(X<1)=P(X=0)={ }^{10} C _0\left(\frac{1}{2}\right)^0\left(\frac{1}{2}\right)^{10}=\left(\frac{1}{2}\right)^{10}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.