To find the expected value (EV) in this situation, we calculate the weighted average of the possible outcomes based on their probabilities.

Step 1: Identify the outcomes and probabilities

1. If the architect wins the bid:

   • Revenue: $45,000
   • Cost: $18,000
   • Net profit: $45,000 - 18,000 = 27,000$
   • Probability of this outcome: $0.4$.

2. If the architect does not win the bid:

   • Loss: The cost of preparing and submitting the plans, which is $18,000.
   • Probability of this outcome: $1 - 0.4 = 0.6$.

Step 2: Write the EV formula

$EV = (P_{\text{win}} \times \text{Profit}_{\text{win}}) + (P_{\text{lose}} \times \text{Profit}_{\text{lose}})$

Step 3: Substitute the values

$EV = (0.4 \times 27,000) + (0.6 \times -18,000)$

Step 4: Calculate each term

1. $0.4 \times 27,000 = 10,800$
2. $0.6 \times -18,000 = -10,800$

Step 5: Add the results

$EV = 10,800 - 10,800 = 0$

Conclusion

The expected value of this situation is $0. This means that, on average, the architect neither gains nor loses money from participating in this process.

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Would you like further details or have any questions about this? Here are 5 related questions for exploration:

1. How does the expected value change if the probability of winning increases?
2. What is the breakeven probability for the architect to make this endeavor worthwhile?
3. How would the EV calculation change if the preparation costs were reduced?
4. What other risks might the architect consider beyond financial costs?
5. Can we model this as a decision under risk, and if so, how?

Tip: When assessing financial decisions, consider both expected value and the risks of variability to avoid over-reliance on averages!