Answer: a) 91% b) 9% c) 16%
Step-by-step explanation:
Let A be the event that homes for sale have garages and B be the event that homes for sale have swimming pools.
Now, given :[tex]P(A)=75\%=0.75[/tex]
[tex]P(B)=29\%=0.29[/tex]
[tex]P(A\cap B)=13\%=0.13[/tex]
a) [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow\ P(A\cup B)=0.75+0.29-0.13=0.91[/tex]
Hence, the probability that a home for sale has a pool or a garage is 91%.
b) The probability that a home for sale has neither a pool nor a garage is given by :-
[tex]1-P(A\cup B)=1-0.91=0.09[/tex]
Hence, the probability that a home for sale has neither a pool nor a garage is 9%.
c) The probability that a home for sale has a pool but no garage is given by :-
[tex]P(B)-P(A\cap B)=0.29-0.13=0.16[/tex]
Hence, the probability that a home for sale has a pool but no garage is 16%.
