Question

In a cricket match, a batswoman hits a boundary $6$ times out of $30$ balls she plays. Find the probability that she did not hit a boundary.

Answer 1

Calculate the probability:

The number of boundaries hit by the batswoman, $n\left(B\right)=6$.

The total number of balls, $n\left(S\right)=30$.

Thus, the number of balls without a boundary, $n\left(B\text{'}\right)=n\left(S\right)-n\left(B\right)=\left(30-6\right)=24$.

Hence, the probability that the batswoman did not hit a boundary is $\mathit{P}\mathbf{(}\mathbf{B}\mathbf{\text{'}}\mathbf{)}\mathbf{=}\frac{\mathbf{n}\mathbf{(}\mathbf{B}\mathbf{\text{'}}\mathbf{)}}{\mathbf{n}\mathbf{\left(}\mathbf{S}\mathbf{\right)}}$.

$$\begin{gathered} \Rightarrow P\left(B\text{'}\right)=\frac{24}{30} \\ \Rightarrow P\left(B\text{'}\right)=\frac{4}{5} \end{gathered}$$

Therefore, the probability that the batswoman did not hit a boundary is $\frac{4}{5}$.