Question

A coin is tossed $n$ times. The probability of getting head at least once is greater than 0.8, then the least value of $n$ is

• A. $2$
• B. $3$
• C. $5$
• D. $4$

Answer 1

The correct option is B $3$

Let $X$ be the number of heads getting in $n$ tossed. Therefore $X$ follows binomial distribution with parameters
$n,p=\frac{1}{2},q=\frac{1}{2}$,
Given that $P(X\ge 1)\ge 0.8$
$\therefore 1-P(X=0)\ge 0.8$
$\Rightarrow P(X=0)\le 0.2$
${\Rightarrow }^n{C}_0{\frac{1}{2}}^n{\frac{1}{2}}^0\le 0.2$
$\Rightarrow \frac{1}{2^n}\le \frac{1}{5}$
$\Rightarrow 2^n\ge 5$
$\therefore$ The least value of $n$ is 3.