A fair coin is tossed $n$-times such that the probability of getting at least one head is at least 0

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

Professor PC Thomas Classes · Answer

(4) : Probability of getting at least one head is at least 0.9 .\ $\Rightarrow 1-\left(\frac{1}{2}ight)^{n} \geq 0.9$\ $[\because$ Probability of getting at least one head = 1 - Probability of getting no head]\ $\Rightarrow\left(\frac{1}{2}ight)^{n} \leq 0.1 \Rightarrow(0.5)^{n} \leq 0.1$\ Now, $\begin{aligned}(0.5)^{2} & =0.25,(0.5)^{3}=0.125,(0.5)^{4} \ & =0.0625\end{aligned}$\ $\Rightarrow \quad$ Minimum value of $n$ is 4 .\