In a survey of 100 persons, it was found that 28 read magazine A, 30 r

1.	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: How many read none of three magazines?
Answer» Total number of People n(P) = 100. People who Read Magazine A n(A) =28. People who Read Magazine B n(B) = 30. People who Read Magazine C n(C) = 42. People who Read Magazine A and B n(A ∩ B) = 8 People who Read Magazine B and C n(B ∩ C) = 10 People who v Read Magazine A and C n(A ∩ 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 = 100–20 = 80 People who read none of the three magazines = n(A∪B∪C)’ = n(P) – n(A∪B∪C) = 100 –80 = 20. ∴ People who read no magazine = 20

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: How many read none of three magazines?

Answer»

Total number of People n(P) = 100.

People who Read Magazine A n(A) =28.

People who Read Magazine B n(B) = 30.

People who Read Magazine C n(C) = 42.

People who Read Magazine A and B n(A ∩ B) = 8

People who Read Magazine B and C n(B ∩ C) = 10

People who v Read Magazine A and C n(A ∩ 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

= 100–20

= 80

People who read none of the three magazines

= n(A∪B∪C)’

= n(P) – n(A∪B∪C)

= 100 –80

= 20.

∴ People who read no magazine = 20