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An unbiased coin is tossed $n$ times. If the probability of getting atleast one head is greater than 0.8 , then the least value of $n$ is
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Verified Answer
The correct answer is:
3
The probability of getting at least one head
$$
\begin{aligned}
& =1-(\text { probability of getting no head) } \\
& =1-{ }^n C_n\left(\frac{1}{2}\right)^n=1-\left(\frac{1}{2}\right)^n>0.8 \text { (given), } \\
& \Rightarrow\left(\frac{1}{2}\right)^n < \frac{1}{5} \Rightarrow 2^n>5
\end{aligned}
$$
The least value of $n$ is 3 .
$$
\begin{aligned}
& =1-(\text { probability of getting no head) } \\
& =1-{ }^n C_n\left(\frac{1}{2}\right)^n=1-\left(\frac{1}{2}\right)^n>0.8 \text { (given), } \\
& \Rightarrow\left(\frac{1}{2}\right)^n < \frac{1}{5} \Rightarrow 2^n>5
\end{aligned}
$$
The least value of $n$ is 3 .
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