Question

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

Answer 1

$P($ Head $)=\frac{1}{2}$
$1-P($ All tail $) \geq 0.9$
$1-\left(\frac{1}{2}\right)^{n} \geq 0.9$
$\Rightarrow\left(\frac{1}{2}\right)^{n} \leq \frac{1}{10}$
$\Rightarrow n_{\min }=4$