   # 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 B independent? 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 4, Problem 56SE
Textbook Problem
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## 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 B independent?

a.

To determine

Compute the probability of A .

### Explanation of Solution

Calculation:

The given table provides idea initial asking price and day listed until sold. The company sales 800 home in the previous year. Event A denotes that a home is listed for more than 90 days.

The probability of the event can be obtained as follows:

P(E)=Number of ways event occursTotal frequency

The company sales 800 homes in the previous year and 200 of them are listed for more than 90 days before being sold

b.

To determine

Compute the probability of B.

c.

To determine

Compute the probability of AB.

d.

To determine

Compute the probability that the home will take cooper Reality more than 90 days to sell given that initial asking price is less than \$150,000.

e.

To determine

Check whether events A and B are independent or not. Explain the reason.

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