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 likelihood 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.

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 > 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 Bindependent?

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Days Listed Until Sold Under 30 31-90 Over 90Total Under $150,000 50 20 20 10 40 150 280 30 500 10 80 100 10 100 250 400 50 $150,000-$199,999 $200,000-$250,000 Initial Asking Price Over $250,000 Total 200 800