In a survey of 200 students from 7 different schools, 50 people do not play

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Question

In a survey of 200 students from 7 different schools, 50 people do not play NFS, 40 people do not play Dota and 10 people play no online game. Then find the no. of people out of 200 people who do not play both the games provided these are the only two games on offer.

Options:

A . 80

B . 70

C . 60

D . 50

Answer: Option A
:
A
Let the no. of people who do not play NFS be n(N^I) = 50 (Given)
Similarlyno. of people who do not play Dota be n(D^I) = 40 (Given)
And theno. of people who do not play any gamen(N^I ∩ D^I) = 10 (Given)
We have to find the no. of people who do not play both the games = n(N∩ D)^{I
We know from the Demorgan's law}
(A∩ B)^{I =}A^I ∪B^I
So,n(N∩ D)^{I =}n(N^I) ∪n(D^I)
n(N^I) ∪n(D^I)= n(N^I) +n(D^I)-n(N^I ∩ D^I)
n(N^I) ∪n(D^I) = 50 + 40 - 10
= 80

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