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Question

According to a survey of 500 people, 300 preferred tea while 100 preferred coffee. 50 people preferred both tea and coffee. how many people didn't prefer any of the drinks?

A
350
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B
150
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C
400
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D
None of the above
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Solution

The correct option is B 150
Let, T be the set of people who preferred Tea and C be the set of people who preferred Coffee.

Given : n(T)=300,n(C)=100,n(TC)=50andn(U)=500
To find : No. of people who do not prefer any of drink =n(TC)

We know,
n(TC)=n(T)+n(C)n(TC)
So, n(TC)=300+10050
=350
We also know,
n(TC)+n(TC)=n(U)
n(TC)=500350
=150





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n(A∪B) = n(A) + n(B) − n(A∩B)
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