Question

A fair coin is tossed $n-$times such that the probability of getting at least one head is at least $\mathrm{0.9.}$ Then the minimum value of $n$ is

Answer 1

Probability of getting head in one time $=\frac{1}{2}$
Probability of getting head in $n-$time $={\left(\frac{1}{2}\right)}^n$
Probability of getting at least one head in $n-$time $=1-{\left(\frac{1}{2}\right)}^n$
Now,
$1-{\left(\frac{1}{2}\right)}^n\ge 0.9$
$\Rightarrow \frac{1}{2^n}\le \frac{1}{10}$
$\Rightarrow 2^n\ge 10$
$\therefore n\ge 4$