Let’s solve this step by step.

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Part a: Expected Value Calculation

The expected value (EV) is calculated using the formula:

$\text{EV} = (\text{Probability of success} \times \text{Profit in case of success}) + (\text{Probability of failure} \times \text{Loss in case of failure})$

1. Determine Profit in Case of Success:

If the architect is awarded the bid, she will earn $120,000, but she will have spent $12,000 for the plans and model. The net profit in this case is:

$\text{Profit in case of success} = 120,000 - 12,000 = 108,000$

2. Determine Loss in Case of Failure:

If the architect is not awarded the bid, she loses only the cost of the plans and model, which is:

$\text{Loss in case of failure} = -12,000$

3. Apply Probabilities:

The probability of success is 0.1, and the probability of failure is $1 - 0.1 = 0.9$.

Now calculate the expected value:

$\text{EV} = (0.1 \times 108,000) + (0.9 \times -12,000)$

4. Perform the Calculations:

$\text{EV} = (0.1 \times 108,000) + (0.9 \times -12,000)$ $\text{EV} = 10,800 - 10,800$ $\text{EV} = 0$

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Part b: Interpretation of Expected Value

The expected value is $0. This means the architect neither expects to gain nor lose money in the long run.

The correct statement is:

B. In the long run, the architect would expect to break even.

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Final Answers:

Part a: Expected Value = $0
Part b: Correct Option = B

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Do you want a more detailed explanation of expected value?

Here are 5 related questions to deepen understanding:

1. What is the meaning of "expected value" in probability?
2. How would the expected value change if the probability of success increased?
3. What would happen to the expected value if the cost of plans and a model decreased?
4. Can an expected value of $0 still justify participating in this scenario?
5. How does the probability of success influence risk assessment for the architect?

Tip: Always compare expected value with the cost and potential risks to make informed decisions in similar scenarios.