Question

A realtor who takes the listing on a house to be sold knows that she will spend $900 trying to sell the house. If she sells it herself, she will earn 6% of the selling price. If another realtor sells a house from her list, the first realtor will earn only 3% of the price. If the house remains unsold after 6 months, she will lose the listing. Suppose the probabilities are as follows: What is the Event Probability Sells the house alone 0.50 Sells through another agent 0.30 Does not sell in 6 months 0.20 What is the expected profit from listing a $175,000 house?

Answer 1

The expected profit from listing a $175,000 house is $6,645.

Step-by-step explanation:

To calculate the expected profit from listing a $175,000 house, we need to consider the probabilities and earnings associated with each outcome. Let's break it down step by step:

1. The probability of selling the house alone is 0.50. In this case, the realtor will earn 6% of the selling price, which is $175,000 x 0.06 = $10,500.
2. The probability of selling the house through another agent is 0.30. In this case, the realtor will earn 3% of the selling price, which is $175,000 x 0.03 = $5,250.
3. The probability of not selling the house in 6 months is 0.20. In this case, the realtor will have a loss of $900.

To calculate the expected profit, we multiply each outcome by its probability and add them all together:

Expected Profit = (0.50 x $10,500) + (0.30 x $5,250) - (0.20 x $900) = $5,250 + $1,575 - $180 = $6,645.

Therefore, the expected profit from listing a $175,000 house is $6,645.