SOLUTION: ​Real estate ads suggest that 52% of homes for sale have​ garages, 39% have swimming​ pools, and 10% have both features a) What is the probability that a home for sale has

Algebra.Com
Question 1196638: ​Real estate ads suggest that 52% of homes for sale have​ garages, 39% have swimming​ pools, and 10% 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 it has a​ pool, too?
​c) Are having a garage and having a pool independent​ events? Explain.
​d) Are having a garage and having a pool mutually​ exclusive? Explain
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
Real estate ads suggest that 52% of homes for sale have​ garages, 39% have swimming​ pools, and 10% 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 it has a​ pool, too?
​c) Are having a garage and having a pool independent​ events? Explain.
​d) Are having a garage and having a pool mutually​ exclusive? Explain
~~~~~~~~~~~~~~~~~ 

(a)  P(a home has a​ garage, but not a​ pool) = P(has a garage) - P(have both) = 52% - 10% = 42%.    ANSWER



(b)  This question asks about the conditional probablity

     P(a home has a pool given that it has a garage) = P(has a pool | has a garage) =  =  = .    ANSWER



(d)  Mutually exlusive means "no intersection", or "empty intersection".

     Is the intersection empty in this problem ? - the answer is in the post.



(c)  To check if these events are independent, you should compare the numbers  

         P(garage)*P(pool), from one side, and P(both), from the other side.

     Using the given data in the post, calculate and compare.


     If the numbers are the same, then the events are independent.

     If the numbers are the different, then the events are NOT independent.

In (a) and (b), you have my answers with explanations.
In (c) and (d), you have all needed instructions.



RELATED QUESTIONS

I need help with this problem. Real Estate ads suggest that 53% of homes for sale have (answered by ewatrrr)
A realty company has 100 homes listed for sale.Some of thses homes have fire places, some (answered by stanbon)
A realty company has 100 homes listed for sale.Some of these homes have fire places, some (answered by richwmiller)
Need Help With This Problem.. Thank You!!! 17. In a subdivision, 67% of the homes have... (answered by edjones)
You look at real estate ads for houses in Naples, Florida. There are many houses ranging... (answered by stanbon)
two neighbors,both wilma and betty, each have swimming pools. Both wilma and betty pools... (answered by josmiceli)
A realty company has 100 homes listed for sale.Some of these homes have fire places, some (answered by ewatrrr)
A real estate agent wishes to determine whether tax assessors and real estate appraisers... (answered by math_tutor2020)
A candidate for the position of governor of a midwestern state has an advertising budget (answered by greenestamps)