Question

If $X$ follows a binomial distribution with parameters $n=8$ and $p=\frac{1}{2}$, then find
$P(|X-4|\le 2)$

• A. $\frac{119}{128}$
• B. $\frac{15}{128}$
• C. $\frac{237}{128}$
• D. $\frac{19}{128}$

Answer 1

The correct option is A $\frac{119}{128}$

$P(|X-4|\le 2)=1-P(X=7)-P(X=8)$
$=1{-}^8{C}_7{\left(\frac{1}{2}\right)}^8{-}^8{C}_8{\left(\frac{1}{2}\right)}^8$ $=1-\frac{9}{128}=\frac{119}{128}$