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A construction company has bid on a building renovation project. The company estimates the probabilities of potential profit (or loss) as shown in the table below.

| Profit/Loss | Probability |
|-------------|-------------|
| \[tex]$25,000 | 0.20 |
| \$[/tex]15,000 | 0.25 |
| \[tex]$10,000 | 0.20 |
| \$[/tex]5,000 | 0.15 |
| \[tex]$0 | 0.10 |
| -\$[/tex]5,000 | 0.10 |

What is the profit expectation for the company?



Answer :

GinnyAnswer
To determine the profit expectation for the company, we need to calculate the expected value of the profit (or loss). The expected value is calculated by multiplying each possible profit or loss by its respective probability and then summing these products. Here is a detailed, step-by-step solution:

1. List the potential profits and losses and their corresponding probabilities:

- Profit/Loss: \[tex]$25,000, Probability: 0.20 - Profit/Loss: \$[/tex]15,000, Probability: 0.25
- Profit/Loss: \[tex]$10,000, Probability: 0.20 - Profit/Loss: \$[/tex]5,000, Probability: 0.15
- Profit/Loss: \[tex]$0, Probability: 0.10 - Profit/Loss: -\$[/tex]5,000, Probability: 0.10

2. Calculate the product of each profit/loss and its probability:

- \[tex]$25,000 × 0.20 = \$[/tex]5,000
- \[tex]$15,000 × 0.25 = \$[/tex]3,750
- \[tex]$10,000 × 0.20 = \$[/tex]2,000
- \[tex]$5,000 × 0.15 = \$[/tex]750
- \[tex]$0 × 0.10 = \$[/tex]0
- -\[tex]$5,000 × 0.10 = -\$[/tex]500

3. Sum these products to obtain the expected profit:

[tex]\[ 5,000 + 3,750 + 2,000 + 750 + 0 - 500 = 11,000 \][/tex]

Hence, the profit expectation for the construction company is \$11,000.