Question

Based on past experience, a building contractor sets the probability of winning a contract at 0.30. The contract is worth $25,000 and the cost to prepare the contract proposal is $2400. What is the expected value of the contract proposal?

Question 8 options:

-$5100


$5100


$22600


-$22600

Answer 1

To calculate the expected value of the contract proposal, we need to consider both the potential earnings from winning the contract and the costs associated with preparing the proposal.

1. **Calculate the probability of winning and losing:**
- Probability of winning the contract (P(win)) = 0.30
- Probability of losing the contract (P(lose)) = 1 - P(win) = 1 - 0.30 = 0.70

2. **Calculate the outcomes:**
- If the contractor wins the contract:
- Earnings from the contract = $25,000
- Cost to prepare the proposal = $2,400
- Net gain if successful = $25,000 - $2,400 = $22,600
- If the contractor loses the contract:
- Cost to prepare the proposal = $2,400
- Net loss if unsuccessful = -$2,400

3. **Calculate the expected value (EV):**
\[
EV = (P(win) \times \text{Net gain}) + (P(lose) \times \text{Net loss})
\]
\[
EV = (0.30 \times 22,600) + (0.70 \times -2,400)
\]

Calculate each term:
- Winning outcome: \( 0.30 \times 22,600 = 6,780 \)
- Losing outcome: \( 0.70 \times -2,400 = -1,680 \)

Now, sum these values to get the expected value:
\[
EV = 6,780 + (-1,680) = 6,780 - 1,680 = 5,100
\]

Therefore, the expected value of the contract proposal is **$5,100**.

The correct answer is: **$5,100**.