Question

real estate ads suggest that 67% of homes for sale have garages, 21% have swimming pools, and 11% have both features.

A. what is the probability that a home for sale has a garage, but not a pool?

B. if a home for sale has a garage, what's the probability that is has a pool, too?

C. Are having a garage and having a pool idependent events? Explain.

D. Are having a garage and having a pool mutually exclusive? Explain.

Answer 1

let us define the events as:-

A : homes for sale have garages

B : homes for sale have swimming pools.

given data are :-

A. the probability that a home for sale has a garage, but not a pool is:-

B. if a home for sale has a garage,the probability that is has a pool, too is :-

C.two events A and B are said to be independent , if ,

in this problem,

so, we can say that,  having a garage and having a pool are not independent events.

D. two events A and B are said to be mutually exclusive event if,

in this problem,

so, we have,

having a garage and having a pool are not mutually exclusive.

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