Discuss the below:
Q: 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?