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A survey was conducted to determine the popularity of 3 foods among
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27 Nov 2021, 04:30
27 Nov 2021, 04:30
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A survey was conducted to determine the popularity of 3 foods among students. The data collected from 75 students are summarized as below
48 like Pizza
45 like Hoagies
58 like tacos
28 like pizza and hoagies
37 like hoagies and tacos
40 like pizza and tacos
25 like all three food
What is the number of students who like none or only one of the foods?
A. 4
B. 16
C. 17
D. 20
E. 23
48 like Pizza
45 like Hoagies
58 like tacos
28 like pizza and hoagies
37 like hoagies and tacos
40 like pizza and tacos
25 like all three food
What is the number of students who like none or only one of the foods?
A. 4
B. 16
C. 17
D. 20
E. 23
Re: A survey was conducted to determine the popularity of 3 foods among
[#permalink]
27 Nov 2021, 07:32
27 Nov 2021, 07:32
1
Number of students who like none or only one of the foods = Total surveyed students - Number of students who like at least 2 foods
Total surveyed students = 75
Number of students who like at least 2 foods = P(Pizza ∩ Hoagies) + P(Hoagies ∩ Tacos) + P(Tacos ∩ Pizza) - 2P(Pizza ∩ Hoagies ∩ Tacos)
= 28 + 37 + 40 - 2*25 = 105 - 50 = 55
Therefore, Number of students who like none or only one of the foods = 75 - 55 = 20
Hence, Answer is D
Total surveyed students = 75
Number of students who like at least 2 foods = P(Pizza ∩ Hoagies) + P(Hoagies ∩ Tacos) + P(Tacos ∩ Pizza) - 2P(Pizza ∩ Hoagies ∩ Tacos)
= 28 + 37 + 40 - 2*25 = 105 - 50 = 55
Therefore, Number of students who like none or only one of the foods = 75 - 55 = 20
Hence, Answer is D
Re: A survey was conducted to determine the popularity of 3 foods among
[#permalink]
06 Aug 2024, 23:44
06 Aug 2024, 23:44
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