Question

A construction compan is planning to bid on a building contract. The bid costs the company $1500. The probability that the bid is accepted is 2. If the bid is accepted, the company will make $11,250 minus the cost of the bid. What is the expected value in this situation?

Answer 1

To calculate the expected value of the bidding situation, we first need to clarify the information given:

1. **Cost of Bid:** $1,500
2. **Probability of Acceptance:** It seems there is a misunderstanding with "the probability that the bid is accepted is 2." Probabilities should be between 0 and 1. Let’s assume the probability of acceptance is 0.2 (20%) for this calculation. If you meant something different, please clarify.
3. **Payoff if Accepted:** $11,250 (profit) - $1,500 (cost of the bid) = $9,750 net profit if the bid is accepted.
4. **Payoff if Rejected:** The company loses the cost of the bid which is $1,500.

Using these clarifications, we calculate the expected value (EV) using the formula:

\[
\text{EV} = (P(\text{accepted}) \times \text{Payoff if accepted}) + (P(\text{rejected}) \times \text{Payoff if rejected})
\]

Where
- \( P(\text{rejected}) = 1 - P(\text{accepted}) \)

Assuming the probability of acceptance \( P(\text{accepted}) = 0.2 \):
\[
P(\text{rejected}) = 1 - 0.2 = 0.8
\]

Now substituting the numbers into the expected value formula:

\[
\text{EV} = (0.2 \times 9750) + (0.8 \times -1500)
\]
\[
\text{EV} = (0.2 \times 9750) + (0.8 \times -1500)
\]
\[
\text{EV} = 1950 - 1200
\]
\[
\text{EV} = 750
\]

The expected value of the bidding situation under these assumptions is **$750**.

If the probability of acceptance needs to be changed or if you have additional information, please update me, and I can re-calculate accordingly!