Question

In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the drinks. how many people like both coffee and tea

Answer 1

19 people both like coffee and tea. Let me explain.

Let’s use the letter “C” for the set op people who like coffee, and let’s use T for the set of people who like tea.

People who like coffee: n(C) = 37

People who like tea: n(T) = 52

Number of people who like at least coffee or tea = n(C U T) = 70

Number of people who like both coffee and tea = n(C , T) = ?

We know that:

n(C U T) = n(C) + n(T) - n(C , T)

70 = 37 + 52 - n(C , T)

70 = 89 - n(C , T)

n(C , T) = 89 - 70

n(C , T) = 19

Therefore 19 like both coffee and tea

Answer 2

Hope u like my process
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Let event A be the people who like coffee

Let event B be the people who like tea.

So,

People liking one of the two = (AUB)

So people liking both = (A, B)

By problem,
=-=-=-=-=-=-=-
=> (A) = 37

=> (B) = 52

=> (A U B) = 70

=> (A, B) =(A) +(B) - (AUB)

or, (A, B) = 37+52-70 = 19

So the required peoples who likes both =19

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