1. **State the problem:** We have a bag with 7 red, 5 blue, and 4 green marbles, totaling $7 + 5 + 4 = 16$ marbles. We draw 3 marbles without replacement and want the probability that all 3 are red. 2. **Formula for probability without replacement:** $$P(\text{all red}) = \frac{\text{number of ways to choose 3 red marbles}}{\text{number of ways to choose any 3 marbles}} = \frac{\binom{7}{3}}{\binom{16}{3}}$$ 3. **Calculate combinations:** $$\binom{7}{3} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35$$ $$\binom{16}{3} = \frac{16 \times 15 \times 14}{3 \times 2 \times 1} = 560$$ 4. **Calculate probability:** $$P = \frac{35}{560}$$ 5. **Simplify fraction:** $$P = \frac{\cancel{35}}{\cancel{560}} = \frac{1}{16}$$ 6. **Convert to decimal:** $$P = 0.0625$$ 7. **Round to nearest 1000th:** $$0.0625 \approx 0.063$$ **Final answer:** The probability that all three marbles drawn are red is approximately $0.063$.