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Ex.15.1 Q1 Probability Solution - NCERT Maths Class 9

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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.

 Video Solution
Probability
Ex exercise-15-1 | Question 1

Text Solution

What is known?

Total number of balls played and number of times the batswoman hits boundary.

What is unknown?

Probability of the batswoman not hitting a boundary.

Reasoning:

If the batswoman hits a boundary \(6\) times out of \(30\) balls then she will not hit a boundary in the remaining \(24\) balls.

The empirical probability \(P(E)\) of an event \(E\) happening, is given by:

\(\begin{align}{P}({E})=\frac{ \begin{bmatrix} \text { Number of trials  in which }\\ \text{the event happened } \end{bmatrix} }{ \begin{bmatrix} \text { The total number} \\ \text{of trials } \end{bmatrix} }\end{align}\)

Steps:

Number of balls played \(= 30\)

Number of balls the batswoman hits boundary \(= 6\)

Number of balls the batswoman does not hit a boundary \(= 30 - 6 = 24\)

\(P\)(bats - woman does not hit the boundary)
\[\begin{align} &  = \frac{ \begin{bmatrix}\text{Number of times the bats-woman}\\ \text{ does not hit the boundary}   \end{bmatrix}} {\text{Number of balls played}} \\ & = 24/30  \\ &= 4/5   \end{align}\]

  
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