As part of a campaign to encourage us to eat more fruit every day a random survey of shoppers was conducted at a supermarket to find out how many consumers bought different types of fruit on a given day: 5 consumers bought oranges, apples, and bananas 12 bought apples and oranges 13 bought oranges and bananas 20 bought apples and bananas 30 bought apples 40 bought oranges 30 bought bananas (a) Draw a Venn diagram to clearly illustrate the above information (b) How many consumers buy at least one of these fruits? (c) How many consumers buy exactly one of these fruits? (d) How many consumers buy only bananas? (e) How many consumers bought apples and bananas but not oranges? (f) How many consumers were surveyed? Explain.
Question
As part of a campaign to encourage us to eat more fruit every day a random survey of shoppers was conducted at a supermarket to find out how many consumers bought different types of fruit on a given day: 5 consumers bought oranges, apples, and bananas 12 bought apples and oranges 13 bought oranges and bananas 20 bought apples and bananas 30 bought apples 40 bought oranges 30 bought bananas (a) Draw a Venn diagram to clearly illustrate the above information (b) How many consumers buy at least one of these fruits? (c) How many consumers buy exactly one of these fruits? (d) How many consumers buy only bananas? (e) How many consumers bought apples and bananas but not oranges? (f) How many consumers were surveyed? Explain.
Solution
(a) As a text-based AI, I'm unable to draw a Venn diagram. However, I can explain how to do it. You would draw three overlapping circles, each representing one of the fruits: apples, oranges, and bananas. The overlapping sections would represent the consumers who bought more than one type of fruit. For example, the section where all three circles overlap would represent the 5 consumers who bought all three types of fruit.
(b) To find out how many consumers buy at least one of these fruits, you would add up all the consumers: 5 (all three fruits) + 12 (apples and oranges) + 13 (oranges and bananas) + 20 (apples and bananas) + 30 (apples only) + 40 (oranges only) + 30 (bananas only) = 150 consumers.
(c) To find out how many consumers buy exactly one of these fruits, you would add up the consumers who bought only one type of fruit: 30 (apples only) + 40 (oranges only) + 30 (bananas only) = 100 consumers.
(d) The number of consumers who buy only bananas is 30.
(e) To find out how many consumers bought apples and bananas but not oranges, you would subtract the number of consumers who bought all three fruits from the number of consumers who bought apples and bananas: 20 (apples and bananas) - 5 (all three fruits) = 15 consumers.
(f) The total number of consumers surveyed would be the same as the number of consumers who bought at least one of these fruits, which is 150. This is because every consumer bought at least one type of fruit.
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