Question

A coin is tossed twice. The probability of getting head both the times is

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{3}{4}$
• D. $1$

Answer 1

The correct option is B

$\frac{1}{4}$

An explanation for the correct answer:

Step 1: Find the sample space and possible set of outcomes for given event.

We have been given that a coin is tossed twice.

$$\begin{gathered} \Rightarrow S=\{HH,HT,TH,TT\} \\ \Rightarrow n\left(S\right)=4 \end{gathered}$$

We need to find the probability of getting head both times.

Let event $A$: getting head both the times

$$\begin{gathered} \Rightarrow A=\left\{HH\right\} \\ \Rightarrow n\left(A\right)=1 \end{gathered}$$

Step 2: Find the required probability.

the probability of getting head both times would be,

$$\begin{gathered} \Rightarrow P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)} \\ \Rightarrow P\left(A\right)=\frac{1}{4} \end{gathered}$$

Therefore, option (B) is the correct answer.