Question

A coin is tossed n times. If the probability of getting at least one head is atleast $99\%$, then the minimum value of n is?

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

The correct option is B $7$

$P\left(H\right)=\frac{1}{2}$, probability of getting at least one head $=1-P$(No head) $\ge .99$.
$\therefore 1-\frac{1}{2^n}\ge \frac{99}{100}\Rightarrow \frac{1}{2^n}\le \frac{1}{100}\Rightarrow 2^n\ge 100\Rightarrow n\ge 7$.
$\therefore$ Minimum value of $n=7$.