Your company bids on two contracts. You believe the probability that you get the first contract is 0.75 and if you get the first contract the probability that you also get the second one is 0.4. If you do not get the first contract the probability that you get the second one is 0.45. If you get both contracts the profit will be $75,000 for the company, if you get only one the profit will be $15,000. It costs the company $10,000 per contract to make a bid. What is the expected profit for the company?

Question

Your company bids on two contracts. You believe the probability that you get the first contract is 0.75 and if you get the first contract the probability that you also get the second one is 0.4. If you do not get the first contract the probability that you get the second one is 0.45. If you get both contracts the profit will be $75,000 for the company, if you get only one the profit will be $15,000. It costs the company $10,000 per contract to make a bid. What is the expected profit for the company?

Answer 1

To calculate the expected profit for the company, we need to consider the probabilities and profits associated with each possible outcome.

Let's denote:
- Getting the first contract as event A
- Getting the second contract as event B

We are given the following probabilities and profits:
P(A) = 0.75 (Probability of getting the first contract)
P(B|A) = 0.4 (Probability of getting the second contract given that the first contract is obtained)
P(B|~A) = 0.45 (Probability of getting the second contract given that the first contract is not obtained)
Profit(A and B) = $75,000 (Profit if both contracts are obtained)
Profit(A or B) = $15,000 (Profit if only one contract is obtained)
Cost = $10,000 (Cost per bid)

Now, let's calculate the expected profit:

Expected profit from both contracts:
P(A and B) = P(A) * P(B|A) = 0.75 * 0.4 = 0.3
Profit(A and B) = $75,000
Expected profit from both contracts = P(A and B) * Profit(A and B) = 0.3 * $75,000 = $22,500

Expected profit from only one contract:
P(A or B) = P(A) * P(B|A') + P(A') * P(B|~A) = 0.75 * (1 - 0.4) + 0.25 * 0.45 = 0.55
Profit(A or B) = $15,000
Expected profit from only one contract = P(A or B) * Profit(A or B) = 0.55 * $15,000 = $8,250

Total Cost:
Total cost = Cost * (Number of bids) = $10,000 * 2 = $20,000

Expected profit:
Expected profit = (Expected profit from both contracts + Expected profit from only one contract) - Total cost
Expected profit = ($22,500 + $8,250) - $20,000
Expected profit = $30,750 - $20,000
Expected profit = $10,750

Therefore, the expected profit for the company is $10,750.