Question

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than $99\%$ is :

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is C $7$

Let $n$ be the minimum number of toss required to get at least one head, then required probability$=1-$probability that on all $n$ toss we are getting tail.

So, the probability to get at least one head
$=1-P\left(\text{no head}\right)>\frac{99}{100}$
$\Rightarrow 1-{\left(\frac{1}{2}\right)}^n>\frac{99}{100}$
$\Rightarrow {\left(\frac{1}{2}\right)}^n<\frac{1}{100}$
$\Rightarrow 2^n>100$
$\Rightarrow n\ge 7$

Minimum value of $n$ is $7$.