Answer:
Option A
Explanation:
Using Binomial distribution,
$P(X\geq2)=1-P(X=0)-P(X=1)$
= $1-\left(\frac{1}{2}\right)^{n}-\left[^{n}C_{1}.\left(\frac{1}{2}\right).\left(\frac{1}{2}\right)^{n-1}\right]$
= $1-\frac{1}{2^{n}}-^{n}C_{1}.\frac{1}{2^{n}}=1-\left(\frac{1+n}{2^{n}}\right)$
Given, $P(X\geq2)\geq0.96$
$\therefore$ $1-\frac{(n+1)}{2^{n}}\geq\frac{24}{25}\Rightarrow\frac{n+1}{2^{n}}\leq\frac{1}{25}$
$\therefore$ n=8
