Question

In a survey of 120 students, it was found that 17 drink neither tea nor coffee, 88 drink tea and 26
drink coffee. By drawing a Venn-diagram, find out the number of students who drink both tea and
coffee.
Please give me full process answer

Answer 1

Venn diagram in figure

✰✰|| Given ||✰✰

• No. of students in survey = 120

• No. of students not drink tea or coffee = 17

• No. of people drink tea = 88

• No. of people drink coffee = 26

✰✰|| To Find ||✰✰

• No. of students drink tea or coffee

• No. of students drink both tea or coffee

✪|| Solution ||✪

No. of students drink tea or coffee = 120 - 17

↬ No. of students drink tea or coffee = 103

No. of students drink both tea or coffee = (88 + 26) - 103

→ No. of students drink both tea or coffee = 114 - 103

→ No. of students drink both tea or coffee = 11

No. of students drink both tea or coffee = 11

Answer 2

Answer:

Given that :

• n(U) = 120
• n(T) = 88
• n(C) = 26
• n(N) = 17

We need to find :

• n(T∩C) = ?

Solution :

Cardinality of the union set is given to be 120.

From these 120 students, 88 prefer tea and 26 prefer coffee.

Hence, total number of students who preferred at least one thing = 88 + 26 = 114. [ n(T) + n(C) ]

Now, also out of these 120 students, there were 17 people who neither prefer tea nor coffee.

But also out of these 120 students, there was some students who preferred both tea and coffee.

So, these people can be included under intersection of sets of people who preferred only coffee and only tea.

So, by the Formula : n(A U B) = n(A) + n(B) - n(A∩B).

➸ n(T U C) = n(T) + n(C) - n(T∩C)

As we need to find n(T∩C), we will rearrange the formula.

➸ n(T∩C) = n(T) + n(C) - n(T U C)

➸ n(T∩C) = 114 - n(T U C)

➸ n(T∩C) = 114 - (120 - 17)

➸ n(T∩C) = 114 - (103)

➸ n(T∩C) = 11

Hence, number of students who prefer both tea and coffee are 11.

Refer the attachment for Venn Diagram.