In a club of 55 athletes, 35 played cricket and 32 played football. Each athlete played either cricket or football. Find the number of athletes who played: (a) Both Cricket and Football (b) cricket only b) football only

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Question

In a club of 55 athletes, 35 played cricket and 32 played football. Each athlete played either
cricket or football. Find the number of athletes who played:
(a) Both Cricket and Football
(b) cricket only
b) football only

Expert Solution
Step 1

Let A be the event for athletes who played cricket 

And B be the event for athletes who played football

Given 

n(AUB)=55, n(A)=35 and n(B)=32 

Farmula

n(AUB)=n(A)+n(B)-n(A⋂B) 

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