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leonid [27]
3 years ago
10

Real estate ads suggest that 75 % of homes for sale have​ garages, 29 % have swimming​ pools, and 13 % have both features. What

is the probability that a home for sale has ​a) a pool or a​ garage? ​b) neither a pool nor a​ garage? ​c) a pool but no​ garage?
Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
8 0

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 :P(A)=75\%=0.75

P(B)=29\%=0.29

P(A\cap B)=13\%=0.13

a) 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

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 :-

1-P(A\cup B)=1-0.91=0.09

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 :-

P(B)-P(A\cap B)=0.29-0.13=0.16

Hence, the probability that a home for sale has a pool but no​ garage is 16%.

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