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Chapter 11: Problem 6

A construction company is planning to bid on a building contract. The bid costs the company \(\$ 1500\). The probability that the bid is accepted is \(\frac{1}{5}\). If the bid is accepted, the company will make \(\$ 40,000\) minus the cost of the bid. Find the expected value in this situation. Describe what this value means.

Short Answer

Expert verified
The expected value in this situation is \$ 5,500, which means the company can, on average, expect to make \$ 5,500 from each contract they bid on when considering the cost and the probabilities.

Step by step solution

01

Identify the possible outcomes

There are two possible outcomes in this situation: the bid is accepted (with a probability of \(\frac{1}{5}\)) and the company makes a profit, or the bid is not accepted (with a probability of \(\frac{4}{5}\)) and the company loses the cost of the bid. The profit if the bid is accepted is \(\$ 40,000 - \$ 1500\ = \$ 38,500\). The loss if the bid is not accepted is \(-\$ 1500\).
02

Calculate the expected value

The formula for expected value is \(\sum [outcome(i) * probability(i)]\), where \(i\) ranges over all possible outcomes. The expected profit if the bid is accepted is \(\$ 38,500 * \frac{1}{5}\ = \$ 7,700\). The expected loss if the bid is not accepted is \(-\$ 1500 * \frac{4}{5}\ = -\$ 1200\). Thus, the total expected value is \$ 7,700 - \$ 1200 = \$ 5,500.
03

Interpret the result

The expected value of \$ 5,500 means that, on average, the company can expect to make \$ 5,500 from each contract they bid on, taking into account the cost of the bid and the probabilities of the bid being accepted or not. However, it's important to note that this does not mean the company will make \$ 5,500 on every contract. Rather, this is the average outcome over many contracts.

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