1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# In a survey of 100 persons it was found that 28 read magazine A, 30 read magazine B, 42 read magazine C, 8 read magazines A and B, 10 read magazines A and C, 5 read magazines B and C and 3 read all the three magazines. Find : (i) How many read none of three magazines ? (ii) How many read magazine C only ?

Open in App
Solution

## (i) Let n (P) denote total number of persons n(A) denote number of people who read magazine A n(B) denote number of people who read magazine B and n(C) denote number of people who read magazine C Then, n(P) = 100, n(A)= 28, n(B) = 30, n(C)= 42, n(A∩B) = 8, n(A∩C)=10,n(B∩C)=5,n(A∩B∩C)=3 Now, n(A∪B∪C)=n(A)+n(B)+n(C)− n(A∩B)−n(B∩C)−n(A∩C)+n(a∩B∩C) = 28+30+42-8-10-5+3 = 100-23+3 = 100-20 = 80 ∴ Number of people who read none of the three magazines. = n(A∪B∪C) = n(P)−n(A∪B∪C) = 100-80 = 20 Hence, 20 people read none of the three magazines. (ii) n (C only) = 42 - (7+3+2) = 42-12 = 30

Suggest Corrections
5
Join BYJU'S Learning Program
Related Videos
Cardinal Properties
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program