Probability of Real-estate being Sold

Cooper Realty is a small real estate company located in Albany, New York, specializing primarily in residential listings. They recently became interested in
determining the liklihood of one of their listings being sold within a certain number of days. An analysis of company sales of 800 homes in previous years produced
the following data.

Days Listed Until Sold
Under 30 31-90 Over 90 Total
Under $150,000 50 40 10 100
Initial Asking Price $150,000 - $199,000 20 150 80 250
$200,000 - $250,000 20 280 100 400
Over $250,000 10 30 10 50
Total 100 500 200 800

a. If A is defined as the event that a home is listed for more than 90 days before being sold, estimate the probability of A.

b. If B is defined as the event that the initial asking price is under $150,000, estimate the probability of B.

c. What is the probability of A (upside down U meaning "intersecting" B?
P(A) + P(B) - P(A upside down u B )

d. Assuming that a contract was just signed to list a home with an initial asking price of less than $150,000, what is the probability that the home will take Cooper
Realty more than 90 days to sell?

e. Are events A and B independent?

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