A contractor is considering a project that promises a profit of $38,884 with a probability of 0.62. The contractor would lose (due to bad weather, strikes, and such) of $3,668 if the project fails. What is the expected profit? Round to the nearest cent.
A contractor is considering a project that promises a profit of $38,884 with a probability of 0.62. The contractor would lose (due to bad weather, strikes, and such) of $3,668 if the project fails. What is the expected profit? Round to the nearest cent.


To find the **expected profit**, we need to use the formula for **expected value**:

\[
\text{Expected Profit} = (P_{\text{success}} \times \text{Profit}) + (P_{\text{failure}} \times \text{Loss})
\]

Where:
- $ P_{\text{success}} = 0.62 $ is the probability of success.
- $ \text{Profit} = 38,884 $ is the profit if the project is successful.
- $ P_{\text{failure}} = 1 - P_{\text{success}} = 0.38 $ is the probability of failure.
- $ \text{Loss} = -3,668 $ is the loss if the project fails (since it's a negative amount).

### Step-by-step Calculation:

1. **Profit if successful**:
\[
0.62 \times 38,884 = 24,107.28
\]

2. **Loss if failed**:
\[
0.38 \times (-3,668) = -1,393.84
\]

3. **Expected profit**:
\[
\text{Expected Profit} = 24,107.28 - 1,393.84 = 22,713.44
\]

Thus, the expected profit is **$22,713.44**.

Would you like further details or have any other questions?

Here are 5 related questions for further exploration:
1. What would the expected profit be if the success probability changes to 0.75?
2. How would the expected profit change if the loss increases to $5,000?
3. What is the minimum success probability required for the project to break even?
4. How does the magnitude of loss impact the riskiness of a project?
5. Can you calculate the variance of the project's profit?

**Tip**: In decision-making scenarios, the expected profit gives an average estimate but doesn't account for the risk (variance), so it's often helpful to consider both expected value and risk.

A contractor is considering a project that promises a profit of $38,884 with a probability of 0.62. The contractor would lose (due to bad weather, strikes, and such) $3,668 if the project fails. What is the expected profit? Round to the nearest cent.

Learn how to calculate the expected profit for a project where there is a 62% chance of earning $38,884 and a 38% chance of losing $3,668. This problem involves applying probability and expected value concepts, suitable for Grades 10-12 students.

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