2. Cooper Realty is a small real estate company located in Albany, New York, specializing primarily in residential listings. They have recently become interested in determining the likelihood of one of their listings being sold within a certain number of days. Based on historical data, they produced the following gures based on the past 800 homes sold. Days Listed until Sold Under 20 31-90 Over 90 Total Under $50K 50 40 10 100 $50-$100K 20 150 80 250 $100 - $150K 20 280 100 400 Over :5 150K 10 30 10 50 (a) What is the probability that a randomly selected home is listed over 90 days before being sold? (b) What is the probability that a randomly selected initial asking price is under $50K? (c) What is the probability of both of the previous two events? Are these two events inde- pendent? (d) Assuming that a contract has just been signed to list a home with an initial asking price of less than $100K, what is the probability that the home will take Cooper Realty more than 90 days to sell