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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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In a class of 45 students, 25 play cricket, 20 play football, and 10 play both. How many students play only cricket?
10
15
20
25
15
To find students playing only one sport, simply subtract the number of students who play 'both' from the total number of students playing that specific sport.
Total students = 45, students playing cricket = 25, students playing football = 20, students playing both = 10.
n(Only A)=n(A)−n(A∩B)
To find students playing only one sport, simply subtract the number of students who play 'both' from the total number of students playing that specific sport.
Many students subtract the number of students who play 'both' from the total number of students (45), instead of subtracting it from the specific group (cricket players).
Define the sets
Let C be the set of students who play cricket and F be the set of students who play football. We are given n(C)=25 and n(C∩F)=10.
n(C)=25,n(C∩F)=10
Apply the subtraction rule
The number of students who play only cricket is the total number of cricket players minus those who play both cricket and football.
n(Only C)=n(C)−n(C∩F)
Calculate the result
Substituting the given values into the formula: 25−10=15.
n(Only C)=25−10=15
B is correct because subtracting the 10 students who play both from the 25 students who play cricket leaves 15 students who play only cricket.
This logic is essential for data interpretation questions in competitive exams where you often need to calculate mutually exclusive segments from overlapping sets.