Question

Before ordering food for a company barbecue the president took a poll. She asked people if they would eat the ribs, hamburgers, and corn at the bbq. She polled that 64 people in the company that said they would probably attend. This poll revealed that 59 members would eat ribs, 56 would eat corn, 60 would hamburgers, 55 would eat ribs and corn, 54 would eat corn and hamburgers and 53 would eat all three.

Answer 1

The complete question is as shown in the attached figure 1

The Venn diagram is the attached figure 2

Let: R⇒ribs , H⇒hamburgers and C⇒corn

People would eat all three = 53

People would eat only R and H = 56 - 53 = 3

People would eat only C and H = 54 - 53 = 1

People would eat only R and C = 55 - 53 = 2

People would eat only H = 60 - (53+3+1) = 60 - 57 = 3

People would eat only R = 59 - (53+3+2) = 59 - 58 = 1

People would eat only C = 56 - (53+1+2) = 0

See Vinn diagram.

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a. How many people did not want any of these foods?

people did not want any of these foods = 64 - (53+3+1+2+3+1) = 1

b. How many people would eat ribs but not corn?

people would eat ribs but not corn = 1+3 = 4

c. How many people would eat something as long as it was not a hamburger?

people would eat something as long as it was not a hamburger= 1+2 = 3

d. How many people would eat only corn?

people would eat only corn = 0

e. How many people would eat exactly two foods?

people would eat exactly two foods = 1 + 2 + 1