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 calculate the expected profit per gadget, we can analyze the outcomes based on the company's estimates. Let: - Probability of a working gadget (P(W)) = 97/100 = 0.97 - Probability of a faulty gadget (P(F)) = 3/100 = 0.03 **Profit from a working gadget:** Profit from a working gadget = \( \$2 \) **Loss from a faulty gadget:** Loss from a faulty gadget = \(-\$80\) Now, we calculate the expected profit per gadget: \[ E(P) = (P(W) \times \text{profit from working}) + (P(F) \times \text{loss from faulty}) \] \[ E(P) = (0.97 \times 2) + (0.03 \times -80) \] Calculating the first part: \[ 0.97 \times 2 = 1.94 \] Calculating the second part: \[ 0.03 \times -80 = -2.4 \] Now, combine the two results: \[ E(P) = 1.94 - 2.4 = -0.46 \] Therefore, the expected profit per gadget is \( -0.46 \). **Rounded to two decimal places,** the expected profit per gadget is **\(-\$0.46\)**. This means the company can expect a loss in the long term based on its current faulty gadget rate and profit margins.