Question

emergency A survey was conducted to know the hobby of 220 students of class IX. Out of which 130 students informed about their hobby like rock climbing and 180 students informed about their hobby as sky watching. There are 110 students who follow both 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?no need to draw venn diagram

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