Answer :

Let ,


Total number of People n(P) = 500.


People who watch Basketball n(B) =115.


People who watch Football n(F) = 285.


People who watch Hockey n(H) = 195.


People who watch Basketball and Hockey n(B H) = 50


People who watch Football and Hockey n(H F) = 70


People who watch Basketball and Football n(B F) = 45


People who do not watch any games. n(HBF)= 50


Now,


n(HBF)’ = n(P) – n(HBF)


50 = 500–( n(H)+n(B)+n(F) – n (H B)– n (H F)– n (B F)+ n (H B F))


50 = 500–(285+195+115–70–50–45 +n (H B F))


50 = 500–430 + n (H B F))


n (H B F) = 70–50


n (H B F)) = 20


20 People watch all three games.


Number of people who only watch football


= 285–(50+20+25)


= 285–95


= 190.


Number of people who only watch Hockey


= 195–(50+20+30)


= 195–100


= 95.


Number of people who only watch Basketball


= 115–(25+20+30)


= 115–75


= 40.


Number of people who watch exactly one of the three games


As the sets are pairwise disjoint we can write


= number of people who watch either football only or hockey only or Basketball only


=190+95+40


=325


325 people watch exactly one of the three games.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Mark the correct RD Sharma - Mathematics

Mark the correct RD Sharma - Mathematics

If A and B are twRD Sharma - Mathematics

If A and B are twRD Sharma - Mathematics

A survey shows thRD Sharma - Mathematics

If A = {x : x <spRS Aggarwal - Mathematics

Mark the correct RD Sharma - Mathematics

In a group of 70 RD Sharma - Mathematics

If P and Q are twRD Sharma - Mathematics