1. **State the problem:** We have a box with 4 red, 2 white, and 2 green balls. Two balls are drawn one after the other without replacement. We want to find the probability that both balls drawn are the same color. 2. **Formula and rules:** The probability of both balls being the same color is the sum of the probabilities of drawing two red balls, two white balls, or two green balls. The probability of drawing two balls of the same color is: $$P = P(\text{2 red}) + P(\text{2 white}) + P(\text{2 green})$$ 3. **Calculate total number of balls:** $$\text{Total balls} = 4 + 2 + 2 = 8$$ 4. **Calculate each probability:** - Probability of 2 red balls: $$P(\text{2 red}) = \frac{4}{8} \times \frac{3}{7} = \frac{12}{56}$$ - Probability of 2 white balls: $$P(\text{2 white}) = \frac{2}{8} \times \frac{1}{7} = \frac{2}{56}$$ - Probability of 2 green balls: $$P(\text{2 green}) = \frac{2}{8} \times \frac{1}{7} = \frac{2}{56}$$ 5. **Sum the probabilities:** $$P = \frac{12}{56} + \frac{2}{56} + \frac{2}{56} = \frac{16}{56}$$ 6. **Simplify the fraction:** $$\frac{16}{56} = \frac{\cancel{8} \times 2}{\cancel{8} \times 7} = \frac{2}{7}$$ **Final answer:** The probability that both balls drawn are the same color is **$\frac{2}{7}$**.