A store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates a yearly proiit of \( \$ 825,000 \) if successful and a yearly loss of \( \$ 275,000 \) otherwise. The probability of success is \( \frac{1}{2} \). If the second mall is selected, it is estimated that the yearly profit will be \( \$ 550,000 \) if successful; otherwise, the annual loss will be \( \$ 165,000 \). The probability of success at the second mall is \( \frac{3}{4} \). Which mall should be chosen in order to maximize the expected profit? The \( \square \) expected proint for the second mall is \( \$ \square \).

To determine which mall to choose in order to maximize the expected profit, let's calculate the expected profit for both malls using the probabilities of success and loss. For the first mall: - Expected profit if successful: \( \$825,000 \) - Expected loss if unsuccessful: \( -\$275,000 \) - Probability of success: \( \frac{1}{2} \) - Probability of failure: \( \frac{1}{2} \) Calculating the expected profit: \[ E_1 = \left(\frac{1}{2} \times 825,000\right) + \left(\frac{1}{2} \times -275,000\right) \] \[ E_1 = 412,500 - 137,500 = 275,000 \] For the second mall: - Expected profit if successful: \( \$550,000 \) - Expected loss if unsuccessful: \( -\$165,000 \) - Probability of success: \( \frac{3}{4} \) - Probability of failure: \( \frac{1}{4} \) Calculating the expected profit: \[ E_2 = \left(\frac{3}{4} \times 550,000\right) + \left(\frac{1}{4} \times -165,000\right) \] \[ E_2 = 412,500 - 41,250 = 371,250 \] Based on the calculations, the expected profit for the second mall is \( \$371,250 \). So, the store should select the second mall to maximize the expected profit. The expected profit for the second mall is \( \$371,250 \).