A survey was conducted to know the hobby of 220 students of class 9. out of which 130 students informed about their hobby as rock climbing and 180 students informed about their hobby as sky watching. there are 110 students follow both the hobbies. then how many students do not have any of two hobbies? how many of them follow the hobby of rock climbing only? How many students follow the hobby of sky watching only?
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Answered by
2
Let A be rock climbing hobby =130
Let B be the sky watching hobby =180
n(A∩B)=110
Total students (U)=220
Hence
n(A∪B)=n(A)+n(B)−n(A∩B)
=130+180−110
=200
Let n(A∪B)
′
= Who do not have either hobby
n(A∪B)
′
=n(U)−n(A∪B)
=220−200
=20
Therefore 20 students do not have both hobby
Student's who only like rock climbing =n(A)−n(A∩B)
=130−110
=20
Students who only like sky watching =n(B)−n(A∩B)
=180−110
=70
Answered by
1
Correct answer:-
Let A be rock climbing hobby =130
Let B be the sky watching hobby =180
n(A∩B)=110
Total students (U)=220
Hence
n(A∪B)=n(A)+n(B)−n(A∩B)
=130+180−110
=200
Let n(A∪B)
′
= Who do not have either hobby
n(A∪B)
′
=n(U)−n(A∪B)
=220−200
=20
Therefore 20 students do not have both hobby
Student's who only like rock climbing =n(A)−n(A∩B)
=130−110
=20
Students who only like sky watching =n(B)−n(A∩B)
=180−110
=70
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