Question

A fair coin is tossed $n$ number of times. If the probability of having at least one head is more than 90%, then $n$ is greater than or equal to

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (C)

4

Answer 2

Since, the probability of getting at least one
head in ?n? tosses $=1-\left(\frac{1}{2}\right)^{n}$, therefore
$1-\left(\frac{1}{2}\right)^{n} \ge\,0.9$
$\Rightarrow \left(\frac{1}{2}\right)^{n} \le0.1$
$\Rightarrow \left(\frac{1}{2}\right)^{n} \le\,0.1$
$\Rightarrow 2^{n} \ge\,10$
$\Rightarrow n \ge\,4$
Hence, the least value of ?n ? is $4$