Question

Real estate ads suggest that 61 % of homes for sale have​ garages, 39 % have swimming​ pools, and 14 % 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.

Answer 1

Answer: a) 0.23, b) No, c) No.

Explanation:

Since we have given that

Probability of homes for sale have garages = 61%

Probability of homes having swimming pool = 39%

Probability of homes having both = 14%

a) If a home for sale has a​ garage, what's the probability that it has a​ pool, too?

Using "Conditional probability", we get that

`P(P|G)=(P(P\cap G))/(P(G))=(0.14)/(0.61)=0.23`

​b) Are having a garage and having a pool independent​ events? Explain.

P(P).P(S) = 0.61×0.39=0.24≠P(P∩S)=0.14

Hence, they are not independent events.

c) Are having a garage and having a pool mutually​ exclusive? Explain.

Since P(P∩S)≠0

So, they are not mutually exclusive.

Hence, a) 0.23, b) No, c) No.