SOLUTION: A realty company has 100 homes listed for sale.Some of these homes have fire places, some have garages, and some have neither. Garage and Fireplace 50 Garage with no fireplace 30

Algebra ->  Probability-and-statistics -> SOLUTION: A realty company has 100 homes listed for sale.Some of these homes have fire places, some have garages, and some have neither. Garage and Fireplace 50 Garage with no fireplace 30      Log On


   

Question 430492: A realty company has 100 homes listed for sale.Some of these homes have fire places, some have garages, and some have neither.
Garage and Fireplace 50
Garage with no fireplace 30
No Garage and fireplace 10
No garage and no fireplace 10
What is the probability that the home selected does not have a fire place?
What is the probabiltiy that the home selected has a fireplace or a garage?
What is the probabiltiy that the home selected had niether a fireplace nor a garage?
What is the probabiltiy that the home selected has a garage but not a fireplace?
What is the probabiltiy that the home selected has a garage, given that it has a fireplace?
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi

A realty company has 100 homes listed for sale

           G-only   F-only       both     neither   Total

status      30        10          50        10       100



P( that the home selected does not have a fire place)= 1 - 60/100 = 40/100

P(that the home selected has a fireplace or a garage) 

 P(A or B) = P(A) + P(B) - P(A and B) = 90/100 - 50/100 = 40/100 

P(that the home selected had neither a fireplace nor a garage)= 10/100

P(that the home selected has a garage but not a fireplace)= 30/100

P(the home selected has a garage, given that it has a fireplace) 

   P(A|B) = P(A and B)/P(B)= 50/100/60/100 = 50/60

may reduce fractions as necessary for classroom format.