Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Real estate ads suggest that 51% of homes for sale have garages, 27% have swimmi

ID: 3019972 • Letter: R

Question

Real estate ads suggest that 51% of homes for sale have garages, 27% have swimming pools, and 17% 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. Yes, because there are no common outcomes.

B. No, because there are outcomes that are common between them.

C. No, because the outcome of one influences the probability of the other.

D. Yes, because the outcome of one does not influence 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

Real estate ads suggest that 51% of homes for sale have garages, 27% have swimming pools, and 17% 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.

Bayee’s theorem used

P=pool, G=Garage

P(P/G) = P( P and G)/P( G)

=0.17/0.51 =0.333

b) Are the events independent?

A. Yes, because there are no common outcomes.

B. No, because there are outcomes that are common between them.

C. No, because the outcome of one influences the probability of the other.

D. Yes, because the outcome of one does not influence 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.