Answer:
a) 0.4
b) 0.28
c) The events are not independent
d) The events are not mutually exclusive
Step-by-step explanation:
Hi!
Lets call:
Gar = {homes with garage}
Pool = {homes with pool},
A = {homes with pool and garage} = Gar ∩ Pool
The data we are given is:
P(Gar) = 0.56
P(Pool) = 0.27
P(A) = 0.16
a) B = {homes with garage but not pool}. This set B is the set Gar without set A: B = Gar / A
P(B) = P(Gar) - P(A) = 0.4
b) This is a conditional probability:
P(Pool | Gar) = P(Gar ∩ Pool) / P(Gar) = 0.16/0.56 = 0.28
c) To be independent events, it must be, by definition:
P(Gar ∩ Pool) = P(Gar) * P(Pool)
0.16 ≠ 0.56*0.27 = 0.15
Then, the events Gar and Pool are not independent
d) Gar and Pool are not mutually exclusive, because there are houses with both pool and garage. We know that because P(A) is not zero.
