Apple products have become a household name in America with

Apple products have become a household name in America with 51 percent of all households owning at least one Apple product (CNN, March 19, 2012). The likelihood of owning an Apple product is 61 percent for households with kids and 48 percent for households without kids. Suppose there are 1,200 households in a representative community of which 820 are with kids and the rest are without kids. a. Are the events “household with kids” and “household without kids” mutually exclusive and exhaustive? Yes No b. What is the probability that a household is without kids? (Round your answer to 4 decimal places.) P(Ac) c. What is the probability that a household is with kids and owns an Apple product? (Do not round intermediate calculations. Round your answer to 4 decimal places.) P(A B) d. What is the probability that a household is without kids and does not own an Apple product? (Do not round intermediate calculations. Round your answer to 4 decimal places.) P(AC Bc)

Solution

a)

Yes.

They can\'t happen at the same time (exclusive) and make up all cases (exhaustive).

b)

P(without kids) = 1 - 820/1200 = 0.316666667 [ANSWER]

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c)

Let

K = with kids
A = owns apple

Thus,

P(A n K) = P(K) P(A|K) = (820/1200)*0.61 = 0.416833333 [ANSWER]

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d)

P(K\' n A\') = P(K\') P(A|K\') = (1-820/1200)*(1-0.48) = 0.164666667 [ANSWER]