Question

In a cricket match, a batsman hits 8 sixes out of $32$ balls played. The probability that a sixes are not hit in a ball is.
A) $ - 0.25$
B) $0.25$
C) $0.75$
D) $0.50$

Answer 1

Hint: From the given information, we can understand that the cricketer hits 6 in some balls and does not hit 6 in other balls. Here, we need to number of favorable balls which the batsman shouldn’t hit a 6, and then we use this to calculate the required probability.

Formula Used:
${\text{Probability of getting an event}} = \dfrac{{{\text{number of favourable outcomes to the event }}}}{{{\text{Total number of possibile outcomes}}}}$
Complete step by step solution:
It is given to us that a batsman hits $8$ sixes out of $32$ balls in a cricket match.
We have to find the probability of not hitting six in a ball.
Here, we know that the probability of any occurring event cannot be more than $1$ and the sum of total probability is always $1$ .
So first, we will find out the probability of hitting $8$ sixes out of $32$ balls, which will be:-
${\text{Probability of hitting 6}} = \dfrac{{{\text{number of 6’s in all balls }}}}{{{\text{Total number of balls}}}}$
Now, substitute the values of the possibility of an event occurring which is $8$ and the total number of possibilities which are $32$.
${\text{Probability of hitting 6}} = \dfrac{8}{{32}}$
${\text{Probability of hitting 6}} = 0.25$
So, the probability of an event occurring is $0.25$.
Now, we will find out the probability of an event not occurring by subtracting the probability of the event occurring from the sum of all probabilities of the same event which is always $1$.
Probability of not hitting six$ = 1 - 0.25$
Probability of not hitting six $ = 0.75$

$\therefore$ The probability of not hitting six on a ball is $0.75$.

Note:
We can also find the probability of not hitting sixes with an alternate method.
We have given that the batsman hits 8 sixes out of $32$ balls played, then the number of balls of not hitting six is equal to (total balls - the balls which hit six)\[ = {\text{ }}32 - 8 = 24\].
Now, you can calculate the probability of not hitting six:
\[\dfrac{{24}}{{32}} = 0.75\]
Therefore, the probability of not hitting sixes is $0.75$.