A real estate company in Albany, Georgia, claims that the probabilities that a house listed with the company will be sold under 30 days, between 30-59 days, between 60-89 days, or at least 90 days are 0.20, 0.30, 0.35, and 0.15, respectively.

A real estate company in Albany, Georgia, claims that the probabilities that a house listed with the company will be sold under 30 days, between 30-59 days, between 60-89 days, or at least 90 days are 0.20, 0.30, 0.35, and 0.15, respectively. A summary of the company’s home sales in the past year is as follows:

 Initial Asking Price Days Listed Until Sold Under $50,000 $(50,000-99,999) at least $100,000 0-29 45 85 30 30-59 95 125 85 60-89 125 165 95 >= 90 15 50 45

(a) Apply Bayes’ theorem and estimate appropriate posterior (revised conditional) probabilities (in 4 decimal points) for the events in the situation presented. Provide an Excel Spreadsheet showing your analytical results and the steps taken for your analysis.

(b) With your estimates in your Excel Spreadsheet in (a), answer the following questions (in 4 decimal points):

1. What is the probability that a house will be sold in 60-89 days, if its initial asking price is $75,000?

2. What is the probability that a house will be sold in 90 days or more, if its initial asking price is $150,000?

(c) What are the conditions that must be met for your estimates in (a) above to be valid? Explain how these conditions are met in this case.