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I need answer Immediately pls!!!!!!-example-1

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Given:

Total number of students = 27

Students who play basketball = 7

Student who play baseball = 18

Students who play neither sports = 7

To find:

The probability the student chosen at randomly from the class plays both basketball and base ball.

Solution:

Let the following events,

A : Student plays basketball

B : Student plays baseball

U : Union set or all students.

Then according to given information,


n(U)=27


n(A)=7


n(B)=18


n(A'\cap B')=7

We know that,


n(A\cup B)=n(U)-n(A'\cap B')


n(A\cup B)=27-7


n(A\cup B)=20

Now,


n(A\cup B)=n(A)+n(B)-n(A\cap B)


20=7+18-n(A\cap B)


n(A\cap B)=7+18-20


n(A\cap B)=25-20


n(A\cap B)=5

It means, the number of students who play both sports is 5.

The probability the student chosen at randomly from the class plays both basketball and base ball is


\text{Probability}=\frac{\text{Number of students who play both sports}}{\text{Total number of students}}


\text{Probability}=(5)/(27)

Therefore, the required probability is
(5)/(27).

User AndrewGrant
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