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

The correct option is C

$4$

Explanation for correct option:

Step1. Define events:

The number of times a fair coin tossed$=n$

Possible outcomes of tossing a fair coin$=\left\{\mathrm{Head},\mathrm{Tail}\right\}$

Step2. Calculate the value of $n$

Probability of getting at least one head in $n$ tosses$=1-{\left(\frac{1}{2}\right)}^n$

As per the given condition,

$$\begin{gathered} 1-{\left(\frac{1}{2}\right)}^n\ge 0.9 \\ \Rightarrow {\left(\frac{1}{2}\right)}^n\le 0.1 \\ \Rightarrow 2^n\ge 10 \\ \Rightarrow n\ge 4 \end{gathered}$$

Hence, Option(C) is the correct answer.