Question

In a cricket, 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

Number of balls the batswoman does not hit a boundary$=30-6=24$.
$P$(She does not hit the boundary)$=\dfrac{24}{30}=\dfrac{4}{5}$.
Let us understand this problem by finding the terms needed for finding the probability that she did not hit a boundary. For this, we need an event and a sample space. So the event will be that the batswoman did not hit a boundary and sample space will be the balls she played.

Complete step by step answer:
Let us consider $E$ to be an event that the batswoman does hit a six and $S$ be the sample space of the balls she played.
Here, the total number balls she played is $30$ out of which the batswoman hit a boundary $6$ times. It means she hit a boundary $6$ times in $6$ balls, and in the remaining balls she did not hit a boundary.
So we can write it as,
Total number of balls the batswoman played$=30$.
Number of times the batswoman hit a boundary$=6$.

We will use these terms to find the number of balls the batswoman does not hit a boundary.
So, the number of times the batswoman does not hit a boundary $=30-6=24$.
As is $E$ the event that the batswoman does not hit a six, therefore $n\left( E \right)=24$.
Also, $S$is the sample space of balls the batswoman played, therefore $n\left( S \right)=30$.

Now we have $n\left( E \right)$ and $n\left( S \right)$ , so we can find $P\left( E \right)$, i.e., $P$(She does not hit the boundary).
$\therefore$ $P$(She does not hit the boundary)
$=P\left( E \right)$
$=$ $\dfrac{\text{number of balls when she did not hit a boundary}}{\text{total number of balls she played}}$
$=\dfrac{n\left( E \right)}{n\left( S \right)}$
$=\dfrac{24}{30}$
$=\dfrac{4}{5}$.

Hence, the probability that she did not hit a boundary is $\dfrac{4}{5}$.

Note: We can also solve this problem by this method:
Total number of balls played$=30$.
Number of times the batswoman hit a boundary$=6$.

$P$(She does not hit the boundary) $=1-P$(She hit the boundary).
$P$ (She hit the boundary) $=$ $\dfrac{\text{number of balls when she hits a boundary}}{\text{total number of balls she played}}$
$=\dfrac{6}{30}$
$=\dfrac{1}{5}$.
$\therefore$ $P$(She did not hit the boundary)
$=1-P$(She hit the boundary)
$=1-\dfrac{1}{5}$
$=\dfrac{5-1}{5}$
$=\dfrac{4}{5}$.