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Real estate ads suggest that 65% of homes for sale have garages, 27% have swimmi

ID: 3246842 • Letter: R

Question

Real estate ads suggest that 65% of homes for sale have garages, 27% have swimming pools, and 12% have both features. a) If a home for sale has a garage, what's the probability that it has a pool, too? b) Are having a garage and having a pool independent events? Explain. c) Are having a garage and having a pool mutually exclusive? Explain. a) The probability that a home for sale that has a garage also has a pool is (Round to three decimal places as needed.) b) Are the events independent? A. No, because there are outcomes that are common between them. B. Yes, because the outcome of one does not influence the probability of the other. C. Yes, because there are no common outcomes. D. No, because the outcome of one influences the probability of the other. c) Are the events mutually exclusive? A. Yes, because the outcome of one does not influence the probability of the other. B. No, because the outcome of one influences the probability of the other. C. No, because there are outcomes that are common between them. D. Yes, because there are no common outcomes.

Explanation / Answer

Probability                       P(G) =0.65

Sale of Swimming pool =27%

Probability                       P(S) =0.27

Sale of garage and swimming pool is 12%

Probability                       P(GS) =0.12

a) The probability that a home for sale that a garage also has a pool is

                            P(S | G) = P(GS) /P(G)

                                          = 0.12/0.65

                                         =0.185

b) Are the events independents

                            P(GS) =0.12

                            P(G)* P(S) =0.65*0.27 =0.1755

                            P(GS) P(G) *P(S)

so they are not independent

option D is correct

c) are the events mutually exclusive

P(GS) 0 so they are not mutually exclusive(Disjoint)

Option B is correct