Question

A construction company is planning to bid on a building contract. The bid costs the company ​$1,000. The probability that the bid is accepted is 2/5 . If the bid is​ accepted, the company will make ​$7,500 minus the cost of the bid.

Answer 1

The construction company's expected profit for bidding on a building contract is calculated by considering the probability of acceptance and the potential profit or loss. With a bid cost of $1,000 and a net gain of $6,500 if successful, the expected profit is $2,000.

Step-by-step explanation:

The scenario described involves a construction company considering whether to bid on a building contract, with a bid cost of $1,000 and a probability of acceptance at 2/5. If accepted, the company stands to make a net profit of $6,500 (which is $7,500 minus the $1,000 bid cost). To calculate the expected profit (or expected value), we multiply each outcome by its probability and sum these products. The company only has two possible outcomes: getting the contract or not getting it.

If the bid is accepted (2/5 chance), the profit is:
2/5 * $6,500 = $2,600

If the bid is not accepted (3/5 chance), the loss is:
3/5 * -$1,000 = -$600

The expected profit is then:
$2,600 + (-$600) = $2,000

So, the expected profit from bidding on the contract is $2,000.