Question

In a survey of 100 students regarding watching T.V., it was found that 28 watch action movies, 30 watch comedy serials, 42 watch news channels, 8 watch action movies and comedy serials, 10 watch action movies and news channels, 5 watch comedy serials and news channels and 3 watch all the three programs. Draw a Venn diagram to illustrate this information and find​ 1) How many watch news channel only? 2) how many do not watch any of the three programs?

Answer 1

Answer:

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Step-by-step explanation:

Let A: Set of persons who watch action movies

B: Set of persons who watch comedy serials

C: Set of persons who watch news channels

Given, Total person N = 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  

1. Number of students who watch news channels only = n(C) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)  

= 42 - 10 - 5 + 3  

= 45 - 15  

= 30  

2. Number of students who watch none of these = n(A ∪ B ∪ C)  = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)  

= 28 + 30 + 42 - 8 - 10 - 5 + 3  

= 103 - 23  

= 80