3. Forty-five percent of Americans like to cook and 59% ofAmericans like to shop

Question

3. Forty-five percent of Americans like to cook and 59% ofAmericans like to shop, while 23% enjoy both activities. a. Are cooking and shopping mutually exclusive? b. Are cooking and shopping independent? c. Does liking to cook change the probability of liking to shop? That is, does P(B | A)-P(B)? Let A= { respondent likes to cook! Let B = { respondent likes to shop Include a contingency table to help answer the above questions. Support all answers with work and describe your answers in complete sentences.

Explanation / Answer

P(A) = 0.45

P(B) = 0.59

P(A and B) = 0.23

A) no, cooking and shoping are not mutually exclusive, because P(both activities) is not zero.

B) P(A) * P(B) = 0.45 * 0.59 = 0.2655

No, they are not independent events, because P(A and B) is not equal to P(A) * P(B)

C) No. As A and B are not independent, P(B | A) will not be equal to P(B)

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