Question

In as survey of 60 people it is found that 25 like to drink milk ,26 coffee and 26 tea, 11like milk and coffee,8 like coffee and tea and 8 like none of the three

Using a venn diagram
1. Find the number of people who like the three drinks
2. Find the number of people who like exactly one of the three drinks

Answer 1

Answer:

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Answer 2

Given : Complete Question is :

In a survey including 60 people, 25 like milk, 26 like tea and 26 like coffee. 9 like both milk and tea, 11 like both milk and coffee, 8 like coffee and milk and 8 like none of the three drinks.

To find :  the number of people who like all the three drinks.

the number of people who like exactly one of the three drinks

Solution:

Total = 60

M = 25

C  = 26

T  = 26

M ∩ T  = 9

M ∩ C  = 11

C ∩ T  = 8

M ∩ T  ∩ C =  like  the three drinks

None =  8

Total  = M + C + T  - M ∩ C - C ∩ T - M ∩ T  + M ∩ T  ∩ C  + None

=> 60 = 25 + 26 + 26 - 11 - 8 - 9 + M ∩ T  ∩ C + 8

=> M ∩ T  ∩ C  = 3

number of people who like the three drinks = 3

number of people who like exactly one of the three drinks = 8 + 10 + 12 = 30

Milk only = M -  M ∩ C - M ∩ T  + M ∩ T  ∩ C

Coffee only = C -  M ∩ C - C ∩ T  + M ∩ T  ∩ C

Tea only = T -  M ∩ T - C ∩ T  + M ∩ T  ∩ C

=>  exactly one of the three drinks =  M + C + T - 2 (  M ∩ C+ C ∩ T + M ∩ T) + 3M ∩ T  ∩ C

= 25 + 26 + 26  - 2( 28) + 3(3)

= 30

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