Answer: a) 0.23, b) No, c) No.
Step-by-step 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
[tex]P(P|G)=\dfrac{P(P\cap G)}{P(G)}=\dfrac{0.14}{0.61}=0.23[/tex]
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.