An airline is considering adding a route to the city of Buffalo, NY. Market research predicts that if the airline serves Buffalo, there is a 32% probability of making a $500,000 profit, a 22% chance of breaking even, and a 46% probability of losing $300,000. What is the expected value of adding a route to Buffalo?


$47,000

$32,000

$25,250

$22,000

To determine the expected value of adding a route to Buffalo, we use the formula for the expected value $ E(X) $ of a discrete random variable, which is:

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

For this problem, the outcomes and their respective probabilities are:

- A 32% (or 0.32 probability) chance of making a \$500,000 profit.
- A 22% (or 0.22 probability) chance of breaking even, which means a profit of \$0.
- A 46% (or 0.46 probability) chance of losing \$300,000.

Now, calculate the expected value:

\[
E(X) = (0.32 \times 500,000) + (0.22 \times 0) + (0.46 \times -300,000)
\]

\[
E(X) = 160,000 + 0 + (-138,000)
\]

\[
E(X) = 160,000 - 138,000 = 22,000
\]

Thus, the expected value of adding a route to Buffalo is **$22,000**.

The correct answer is $22,000.

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

1. What does it mean if the expected value of an investment is positive?
2. How do you interpret the probabilities of different outcomes in decision-making?
3. How would the expected value change if the probability of breaking even was 30%?
4. What is the role of expected value in risk management?
5. How can the airline use expected value in their strategic planning?

**Tip:** Always consider the risk associated with different outcomes when evaluating expected value.

Learn how to calculate the expected value of adding an airline route to Buffalo, NY based on market research probabilities. Understand the mathematical concepts of expected value and probability with a detailed example. Suitable for advanced high school students.

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