in a group of people ,20 like milk,30 likes tea,22like coffee,12 like coffee only,6 like milk and coffee ,2 like tea and coffe only and 8 like milk and tea only.SHOW THESE INFORMATION IN A VENN DIAGRAM AND FIND: (i)how many like atleast on drink? (ii)how many like exactly one drink? in a survey among 100 people ,50 liked coffee,30liked milk,40 liked tea,20 liked coffee only,25 l Iiked tea only,10 liked tea and coffee and 5 liked all tea,,coffee and milk using the venn diagram ,find the number of people who liked neither of these
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Answer:
To represent the given information in a Venn diagram:
Let A represent the set of people who like milk.
Let B represent the set of people who like tea.
Let C represent the set of people who like coffee.
Now, we can use the provided information to fill in the Venn diagram:
- 20 people like milk (A).
- 30 people like tea (B).
- 22 people like coffee (C).
- 12 people like coffee only (C).
- 6 people like milk and coffee (A ∩ C).
- 2 people like tea and coffee only (B ∩ C).
- 8 people like milk and tea only (A ∩ B).
To find the answers to your questions:
(i) To find how many like at least one drink, we need to find the total number of people in the union of sets A, B, and C (A ∪ B ∪ C).
A ∪ B ∪ C = (People who like milk) + (People who like tea) + (People who like coffee) - (People who like exactly two drinks) - (People who like all three drinks)
A ∪ B ∪ C = 20 + 30 + 22 - (6 + 2 + 8) - 0
A ∪ B ∪ C = 56 - 16
A ∪ B ∪ C = 40 people like at least one drink.
(ii) To find how many like exactly one drink, we need to find the sum of people who like only milk, only tea, and only coffee.
People who like only milk = (People who like milk) - (People who like milk and tea only) - (People who like milk and coffee only)
People who like only milk = 20 - 8 - 6
People who like only milk = 6
People who like only tea = (People who like tea) - (People who like tea and coffee only) - (People who like milk and tea only)
People who like only tea = 30 - 2 - 8
People who like only tea = 20
People who like only coffee = (People who like coffee only) - (People who like tea and coffee only) - (People who like milk and coffee only)
People who like only coffee = 12 - 2 - 6
People who like only coffee = 4
Now, sum these up:
6 (like only milk) + 20 (like only tea) + 4 (like only coffee) = 30 people like exactly one drink.
In the survey among 100 people, to find the number of people who liked neither of these drinks, we can subtract the total number of people who liked at least one drink (40) from the total number of people surveyed (100).
Number of people who liked neither of these drinks = Total people surveyed - People who like at least one drink
Number of people who liked neither of these drinks = 100 - 40
Number of people who liked neither of these drinks = 60 people.