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suppose that 55 of all adults regularly consume coffee 45 regularly consume carbonated soft drinks and 70 frequently consu

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Suppose that 55% of all adults regularly consume coffee, 45% regularly consume carbonated soft drinks, and 70% frequently consume at least one of these two products. a) What is the probability that a random adult consumes coffee and soda on a regular basis? b) What is the probability that a random adult does not consume at least one of these two products on a regular basis?

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Answer to a math question Suppose that 55% of all adults regularly consume coffee, 45% regularly consume carbonated soft drinks, and 70% frequently consume at least one of these two products. a) What is the probability that a random adult consumes coffee and soda on a regular basis? b) What is the probability that a random adult does not consume at least one of these two products on a regular basis?

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67 Answers

p(C \cup S) = p(C) + p(S) - p(C \cap S)

0.70 = 0.55 + 0.45 - p(C \cap S)

p(C \cap S) = 0.30

p(\text{not} (C \cup S)) = 1 - p(C \cup S)

p(\text{not} (C \cup S)) = 1 - 0.70

p(\text{not} (C \cup S)) = 0.30

Answer:

\text{(a) } p(C \cap S) = 0.30

\text{(b) } p(\text{not} (C \cup S)) = 0.30

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