Question

In a Cricket match, a batsman hits a boundary 6 times out of 30 balls he
plays. Find the probability that he did not hit a boundary.
​

Answer 1

Given :

In a Cricket match, a batsman hits a boundary 6 times out of 30 balls he plays

To Find :

Probability that he didn't hit a boundary

Solution :

Method - 1 :

Probability of hitting a boundary :

No. of possible outcomes to hit a boundary = 6

Total no. of possible outcomes = 30

$\sf \longrightarrow \dfrac{Number\ of\ possible\ outcomes }{Total\ number\ of\ possible\ outcomes}$

$\sf \longrightarrow \dfrac{6}{30}$

$\sf \longrightarrow\ \dfrac{1}{5}$

Probability of not hitting a boundary :

No. of possible outcomes not to hot a boundary = 30 - 6 = 24

Total no. of possible outcomes = 30

$\longrightarrow \dfrac{30-6}{30}$

$\longrightarrow \dfrac{24}{30}$

$\longrightarrow\ \dfrac{4}{5}$

Method - 2 :

Probability of hitting a boundary :

No. of possible outcomes to hit a boundary = 6

Total no. of possible outcomes = 30

$\longrightarrow\ \dfrac{1}{5}$

Probability of not hitting a boundary :  

$\longrightarrow$  1 - Total no. of possible outcomes

$\longrightarrow 1-\dfrac{1}{5}$

$\longrightarrow\ \dfrac{4}{5}$

Answer 2

Given :

• In a Cricket match, a batsman hits a boundary 6 times out of 30 balls he plays.

To Find :

• Probability that he didn't hit a boundary

Solution :

Probability of hitting a boundry

No. of possible outcomes to hit a boundary :  (6)

Total no. of possible outcomes : (30)

$\boxed{ \rm{provablity \: = \: \frac{number \: of \: outcomes}{total \: number \: of \: out \: comes} }}$

So that,

$\rm \: \dfrac{6}{30}$

$\rm \to \dfrac{6}{30}$

$\rm \: \to \dfrac{1}{5}$

Probability of not hitting a boundary :

No. of possible outcomes not to hit a boundary : 30 - 6 = 24

Total no. of possible outcomes : 30

$\rm\: \dfrac{30 - 6}{30}$

$\to \rm \: \dfrac{24}{30}$

$\rm </strong><strong>\</strong><strong>to</strong><strong>\: \dfrac{</strong><strong>4</strong><strong>}{</strong><strong>5</strong><strong>}$

_______________________________

Also there is another way just an small concept

As we know that total number of output is : $\rm \: \dfrac{30}{30}$

Also we found that number of balls hit to boundary : $\rm \: \dfrac{6}{30}$

To find the number of balls not hit in boundary :

Let (x) be the number of balls not hit to boundary

$\rm \: \dfrac{6}{30} + x = \dfrac{30}{30}$

$\rm \: x = \dfrac{30}{30} - \dfrac{6}{30}$

$\rm \: x = \dfrac{30 - 6}{30}$

$\rm \: x = \dfrac{24}{30}$

$\rm \: x = \dfrac{4}{5} \:[after \ simplification]$