Question

If the probability of 10,000 attendees is 0.25, the probability of 20,000 attendees is 0.4, and the probability of 40,000 attendees is 0.35, determine:

a) the alternative that provide the maximum expected monetary value (emv).

Answer 1

Explanation:

To determine the alternative that provides the maximum expected monetary value (EMV), you need to calculate the expected value for each alternative and then compare them.

The formula for calculating the expected monetary value (EMV) is:

\[ \text{EMV} = \sum_{i} (X_i \cdot P_i) \]

where \(X_i\) is the monetary value of outcome \(i\) and \(P_i\) is the probability of outcome \(i\).

Given the probabilities and monetary values:

- Probability of 10,000 attendees (\(P_1\)): 0.25

- Probability of 20,000 attendees (\(P_2\)): 0.4

- Probability of 40,000 attendees (\(P_3\)): 0.35

- Monetary value for 10,000 attendees (\(X_1\)): $10,000

- Monetary value for 20,000 attendees (\(X_2\)): $20,000

- Monetary value for 40,000 attendees (\(X_3\)): $40,000

Now, calculate the expected monetary value (EMV) for each alternative:

\[ \text{EMV}_1 = (10,000 \cdot 0.25) + (20,000 \cdot 0.4) + (40,000 \cdot 0.35) \]

\[ \text{EMV}_1 = 2,500 + 8,000 + 14,000 \]

\[ \text{EMV}_1 = 24,500 \]

Therefore, the EMV for the alternative with 10,000 attendees is $24,500.

Now, compare this with the other alternatives (if any). The alternative with the maximum EMV is the preferred choice.