Question

In a group of 100 persons, 80 take tea, 30 take coffee and 20 take both of tea and cof- fee. How many persons take neither tea ner coffee? a) 10 b) 12 c) 11 d) 15​

Answer 1

Answer:

Step-by-step explanation:

The total group is of 100 people.

Number of people who drink tea n(T) = 80

People who don’t like tea n(A) = 20

Number of people who drink coffee n© = 30

People who don’t like coffee n(B) = 70

Number of people who take both n(C intersection T) = 20

People who don’t like coffee or tea n(A intersection B) = n(A) + n(B) – n (C intersection T)

20 + 70 – 20

= 70

Answer 2

Answer:

n(U) = 100

n(T) = 80

n(C) = 30

n(T∩C) = 20

n(T∪C) = n(T) + n(C) - n(T∩C) = 80 + 30 - 20 = 90

Now,

n(T∪C)' = n(U) - n(T∪C) = 100 - 90 = 10

The number of persons taking neither coffee nor tea is 10.

Therefore, the correct answer is option (a) 10.