Question

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least $90$% is :

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is C $4$

Let '$n$' number of tosses are required.
$P\left(\text{at least one head}\right)\ge 0.9$
$\Rightarrow 1-{\left(\frac{1}{2}\right)}^n\ge 0.9$
$\Rightarrow \frac{1}{2^n}\le 0.1$

$\Rightarrow 2^n\ge 10$
$\Rightarrow n_{min}=4$