A construction company is planning to bid on a buliding contract. The bid costs the company \( \$ 1600 \). The probability that the bid is accepted is \( \frac{1}{5} \). If the bid is accepted, the company will make \( \$ 25,500 \) minus the cost of the bid. a. What is the expected value in this situation? \( \$ \square \) (Round to the nearest dollar.)

To calculate the expected value of the situation, we first need to consider the potential outcomes. If the bid is accepted (with a probability of \( \frac{1}{5} \)), the profit is \( 25,500 - 1,600 = 23,900 \). If the bid is not accepted (with a probability of \( \frac{4}{5} \)), the company loses the bid cost, so the profit is \( -1,600 \). Now, we can calculate the expected value (EV): \[ EV = (Probability\ of\ accepted\ bid \times Profit\ if\ accepted) + (Probability\ of\ rejected\ bid \times Profit\ if\ rejected) \] \[ EV = \left( \frac{1}{5} \times 23,900 \right) + \left( \frac{4}{5} \times (-1,600) \right) \] Calculating each part: 1. If accepted: \(\frac{1}{5} \times 23,900 = 4,780\) 2. If rejected: \(\frac{4}{5} \times (-1,600) = -1,280\) Now, adding those values together: \[ EV = 4,780 - 1,280 = 3,500 \] So the expected value is \( \$ 3,500 \).