Question

6. In a group of 160 people , 65 do not drink tea, 80 do not drink coffee and
40 people drink both tea and coffee. How may people do not like exactly
one drink?
1) 65
2) 40
3)80
4)95​

Answer 1

Answer:

Step-by-step explanation:

65 do not drink tea, So n(A') =65

80 do not drink coffee, So n(B') =80

and  

40 people drink both tea and coffee

So n(A∩B)=40

Thus n(A)=160-n(A')=160-65=95

n(B)= 160-n(B') = 160-80=80

So n (AUB) = n(A) +n(B) - n(A∩B)

=95+80-40

=175-40=135

Let x are the people who do not like exactly one drink

Then x =160-( who like Tea & coffee +who do not like any of both)

=160-{ n(A∩B)+n( A U B)' }

=160-{ 40+160-n(AUB) }

=160-40-160+n(AUB)

= - 40 + 135=95

Thus 95 people do not like exactly  one drink?