It has been reported that 57% of U.S. households that rent do not have a dishwas

Question

It has been reported that 57% of U.S. households that rent do not have a dishwasher, while only 28% of homeowner households do not have a dishwasher. If one household is randomly selected from each ownership category, determine the probability that Source: Bureau of the Census, Statistical Abstract of the United States 2009, p. 601. neither household will have a dishwasher. both households will have a dishwasher. the renter household will have a dishwasher, but the homeowner household will not. the homeowner household will have a dishwasher, but the renter household will not. A fair coin is tossed three times what is the

Explanation / Answer

a) Let, A be the event that U.S households that rent do not have a dishwasher.

B be the event that home owner households do not have a dishwasher.

Neither households will have a dishwasher.

P(A' and B') = P(A')*P(B')

P(A) = 57% = 0.57

P(B) = 28% = 0.28

P(A') = 1 - P(A) = 1 - 0.57 = 0.43

P(B') = 1 - P(B) = 1 - 0.28 = 0.72

P(A' and B') = 0.43 * 0.72 = 0.3096

b) Both households will have a dishwasher.

P(A and B) = P(A)*P(B) = 0.57*0.28 = 0.1596

c) P(A' and B) = P(A')*P(B) = 0.43*0.28 = 0.1204

d) P(B' and A) = P(B')*P(A) = 0.72*0.57 = 0.4104

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