An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of \( \$ 30,000 \). If the economy grows at a moderate pace, the investment will result in a profit of \( \$ 10,000 \). However, if the economy goes into recession, the investment will result in a loss of \( \$ 30,000 \). You contact an economist who believes there is a \( 30 \% \) probability the economy will remain strong, a \( 60 \% \) probability the economy will grow at a moderate pace, and a \( 10 \% \) probability the economy will slip into recession. What is the expected profit from this investment? The expected profit is \( \$ \square \). (Type an integer or a decimal.)

To find the expected profit, we can calculate it using the probabilities and potential outcomes provided. The expected profit (E) can be calculated as follows: \[ E = (P_{strong} \times Profit_{strong}) + (P_{moderate} \times Profit_{moderate}) + (P_{recession} \times Profit_{recession}) \] Substituting in the values: \[ E = (0.30 \times 30000) + (0.60 \times 10000) + (0.10 \times -30000) \] Calculating each term: - For a strong economy: \( 0.30 \times 30000 = 9000 \) - For a moderate economy: \( 0.60 \times 10000 = 6000 \) - For a recession: \( 0.10 \times -30000 = -3000 \) Now, summing those amounts: \[ E = 9000 + 6000 - 3000 = 12000 \] Thus, the expected profit from this investment is \( \$ 12,000 \).