A company makes electronic gadgets. They estimate that 3 out of every 100 gadgets is faulty, but the company doesn't know which ones are faulty until a buyer complains. Suppose the company makes a \( \$ 2 \) profit on the sale of any working gadget, but suffers a loss of \( \$ 80 \) for every faulty gadget because they have to repair the unit. Check whether the company can expect a profit in the long term. Find the expected profit per gadget. Round your answer to two decimal places.

To find the expected profit per gadget, we can calculate the expected profit for both working gadgets and faulty gadgets based on their probabilities. 1. The probability of a gadget being working is \( \frac{97}{100} \) and the profit from a working gadget is \( \$2 \). 2. The probability of a gadget being faulty is \( \frac{3}{100} \), and the loss from a faulty gadget is \( -\$80 \). Now, we calculate the expected profit per gadget: \[ \text{Expected Profit} = \left(\text{Probability of working} \times \text{Profit from working}\right) + \left(\text{Probability of faulty} \times \text{Loss from faulty}\right) \] \[ \text{Expected Profit} = \left(\frac{97}{100} \times 2\right) + \left(\frac{3}{100} \times -80\right) \] \[ \text{Expected Profit} = \left(0.97 \times 2\right) + \left(0.03 \times -80\right) \] \[ \text{Expected Profit} = 1.94 - 2.4 = -0.46 \] Rounding to two decimal places, the expected profit per gadget is \( -0.46 \). This means that in the long term, the company can expect a loss of \( \$0.46 \) for each gadget produced.