A small software company bids on two contracts. It anticipates a profit of $60,000 if it gets the larger contract and $25,000 if it gets the smaller contract. The company estimates that there is a 32% chance it will get the larger contract and a 62% chance it will get the smaller contract.If the company does not get either of the contracts it will not gain or lose any money. Assuming the contracts will be awarded independently, what's the expected profit?
I am so lost on this...
12
To find the expected profit, we need to calculate the probability-weighted average of the profits for each possible outcome.
Let's break down the problem step by step:
1. Calculate the probability of not getting either contract: Since the total probability must add up to 100%, we can subtract the sum of the probabilities of getting each contract from 100%.
Probability of not getting either contract = 100% - (32% + 62%) = 6%
2. Calculate the expected profit for each scenario:
For the larger contract: Expected profit = Probability of getting the larger contract * Profit if getting the larger contract
Expected profit for the larger contract = 32% * $60,000 = $19,200
For the smaller contract: Expected profit = Probability of getting the smaller contract * Profit if getting the smaller contract
Expected profit for the smaller contract = 62% * $25,000 = $15,500
For not getting either contract, there is no gain or loss, so the expected profit is $0.
3. Calculate the overall expected profit by summing up the expected profits for each scenario:
Overall expected profit = Expected profit for the larger contract + Expected profit for the smaller contract + Expected profit for not getting either contract
Overall expected profit = $19,200 + $15,500 + $0 = $34,700
Therefore, the expected profit for the small software company is $34,700.