Cooper Realty is a small real estate company located in Albany, New York, that specializes primarily in residential listings. The company recently became interested in determining the likelihood of one of its 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 3031–90Over 90Total
Initial Asking PriceUnder $150,00050 40 10 100
$150,000–$199,99920 150 80 250
$200,000–$250,00020 280 100 400
Over $250,00010 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. If required, round your answer to two decimal places.
(b) If B is defined as the event that the initial asking price is under $150,000, estimate the probability of B. If required, round your answer to three decimal places.
(c) What is the probability of A ∩ B? If required, round your answer to four decimal places.
(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? If required, round your answer to two decimal places.
(e) Are events A and B independent?
- Select your answer -YesNo