A restaurant is planning to open in town. The owners estimate that there is a 50% probability that the restaurant will make $50,000, a 15% probability that it will break even, and a 35% probability that it will lose $28,000. Find the expected profit.




The restaurant will lose $10,200.

The restaurant will profit $10,200.

The restaurant will lose $15,200.

The restaurant will profit $15,200.

To find the expected profit for the restaurant, we use the expected value formula:

\[
E(X) = \sum (\text{probability of outcome} \times \text{value of outcome})
\]

Given the probabilities and outcomes:

- A 50% (or 0.50 probability) chance of making \$50,000.
- A 15% (or 0.15 probability) chance of breaking even, which means a profit of \$0.
- A 35% (or 0.35 probability) chance of losing \$28,000.

Now, calculate the expected profit:

\[
E(X) = (0.50 \times 50,000) + (0.15 \times 0) + (0.35 \times -28,000)
\]

\[
E(X) = 25,000 + 0 + (-9,800)
\]

\[
E(X) = 25,000 - 9,800 = 15,200
\]

Thus, the expected profit is **$15,200**.

The correct answer is that the restaurant will **profit $15,200**.

Would you like more details or have any questions? Here are some related questions:

1. How does the expected profit help in making business decisions?
2. What would be the impact on the expected profit if the loss probability increased?
3. How does risk affect the decision to open a new business?
4. Can expected value be used to compare different investment opportunities?
5. What other factors should be considered along with expected value in decision-making?

**Tip:** When assessing expected profit, it's important to also evaluate potential risks and their impacts on the overall financial health of a business.

Learn how to calculate the expected profit for a restaurant opening based on different profit and loss probabilities. Understand the expected value formula and its application in business decision-making. Suitable for advanced high school students.

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