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 30 31–90 Over 90 Total
Initial Asking Price
Under $150,000 50 40 10 100
$150,000–$199,999 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. 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?

The answers are given below

Explanation:

The following analysis can be derived from the question:

(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.

Probability of A will be:

P(A) = 200 / 800

= 1/4

= 0.25

(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.

Probability of B will be:

P(B) = 100 / 800

= 1/8

= 0.125

(c) What is the probability of A ∩ B? If required, round your answer to four decimal places.

The probability of A ∩ B will be that a home is listed for above 90 days and that the initial asking price is also under $150,000. Therefore,

P( A ∩ B) = 10 / 800

= 1/80

= 0.0125

(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.

This will be the probability that a home is listed for more than 90 days based on the condition that the initial asking price of the home is under $150,000. Therefore,

P ( A | B ) = P( A ∩ B) ÷ P(B)

= 0.0125 / 0.125

= 0.1

(e) Are events A and B independent?

No. Events A and B are not independent. This is because P(A) is not equal to P(A|B).

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