Question

4)
A survey was conducted to know the hobby of 220 students of class IX. 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 who follow both the hobbies.
Then how many students do not have any of the 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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Answer 1

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