Cooper Realty is a small real estate company located in Albany New York, special
ID: 3354753 • Letter: C
Question
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. Initial Asking Price Days listed Until Sold Under 30 31-90 Over 90 Total Under $150,000 50 40 10 100 $150,000- $199,999 20 150 80 250 $200,000- 20 280 100 400 $250,000 Over $ 250,000 10 30 10 50 Total 100 500 200 800 1. 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. 2. If B is defined as the event that the initial asking price is under $150,000, estimate the probability of B. 3. What is the probability of A and B? 4. 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? 5. Are events A and B independent? 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. Initial Asking Price Days listed Until Sold Under 30 31-90 Over 90 Total Under $150,000 50 40 10 100 $150,000- $199,999 20 150 80 250 $200,000- 20 280 100 400 $250,000 Over $ 250,000 10 30 10 50 Total 100 500 200 800 1. 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. 2. If B is defined as the event that the initial asking price is under $150,000, estimate the probability of B. 3. What is the probability of A and B? 4. 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? 5. Are events A and B independent?Explanation / Answer
1) probability of A =P(A) =200/800 =0.25
2) probability of B =P(B) =100/800 =0.125
3) probability of A and B =P(AnB) =10/800 =0.0125
4) probability that the home will take Cooper Realty more than 90 days to sell given price of less than $150,000
P(A|B)=10/100 =0.1
5) as we can see that P(AnB) is not equal to P(A)*P(B). therefore A and B are not independent.