Question

The least number of times a coin must be tossed so that the probability of getting atleast one head is atleast $0.8$ is

• A. $6$
• B. $5$
• C. $4$
• D. $3$

Answer 1

The correct option is D $3$

Let $X$ be the number of heads.
$P(X\ge 1)=1-P(X=0)=1-{}^n{C}_0{\left(\frac{1}{2}\right)}^n=1-{\left(\frac{1}{2}\right)}^n$
Given that,
$1-\frac{1}{2^n}\ge 0.8\Rightarrow \frac{1}{2^n}\le 0.2\Rightarrow 2^n\ge \frac{1}{0.2}\Rightarrow 2^n\ge 5$
$\therefore$ Least value of $n$ is $3$