Question

A coin is tossed three times. The probability of getting a head once and a tail twice is

• A. $\frac{1}{8}$
• B. $\frac{1}{3}$
• C. $\frac{3}{8}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C

$\frac{3}{8}$

An explanation for the correct answer:

Step 1: Find the favourable outcomes for given event

We have been given that a coin is tossed three times.

We need to find the probability of getting a head once and a tail twice.

A possible set of outcomes when a coin is tossed three times is,

$$\begin{gathered} S=\left\{\left(HHH\right),\left(HHT\right),\left(HTH\right),\left(HTT\right),\left(THH\right),\left(THT\right),\left(TTH\right),\left(TTT\right)\right\} \\ \Rightarrow n\left(S\right)=8 \end{gathered}$$

Let event $R:$ getting a head once and a tail twice

$$\begin{gathered} R=\left\{\right(HTT),(THT),(TTH\left)\right\} \\ \Rightarrow n\left(R\right)=3 \end{gathered}$$

Step 2: Find the required probability.

probability of getting a head once and a tail twice = number of possible outcomes / total number of outcomes

$$\begin{gathered} \Rightarrow P\left(R\right)=\frac{n\left(R\right)}{n\left(S\right)} \\ \Rightarrow P\left(R\right)=\frac{3}{8} \end{gathered}$$

Therefore, option (C) is the correct answer.