1. **State the problem:** You draw one coin from a bowl containing 13 pennies, 13 dimes, and 24 quarters. We want to find the expected value of the coin drawn. 2. **Formula for expected value:** The expected value $E$ is calculated as $$E = \sum (\text{value of outcome} \times \text{probability of outcome})$$ 3. **Calculate total number of coins:** $$13 + 13 + 24 = 50$$ 4. **Calculate probabilities:** - Probability of penny: $\frac{13}{50}$ - Probability of dime: $\frac{13}{50}$ - Probability of quarter: $\frac{24}{50}$ 5. **Assign values to coins:** - Penny = 0.01 - Dime = 0.10 - Quarter = 0.25 6. **Calculate expected value:** $$E = 0.01 \times \frac{13}{50} + 0.10 \times \frac{13}{50} + 0.25 \times \frac{24}{50}$$ 7. **Calculate each term:** $$0.01 \times \frac{13}{50} = \frac{0.13}{50} = 0.0026$$ $$0.10 \times \frac{13}{50} = \frac{1.3}{50} = 0.026$$ $$0.25 \times \frac{24}{50} = \frac{6}{50} = 0.12$$ 8. **Sum the terms:** $$E = 0.0026 + 0.026 + 0.12 = 0.1486$$ 9. **Round to three decimal places:** $$E \approx 0.149$$ **Final answer:** The expected value of the game is $0.149$.