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.