1. **Problem:** A jar contains 12 red balls, 8 blue balls, and 10 green balls. Two balls are picked without replacement. Find the probability both balls are the same color. 2. **Formula and rules:** The probability of both balls being the same color is the sum of the probabilities of picking two red, two blue, or two green balls. The probability of picking 2 balls of the same color from a group of $n$ balls is $$\frac{\binom{n}{2}}{\binom{30}{2}}$$ where 30 is the total number of balls. 3. **Calculate total number of ways to pick 2 balls:** $$\binom{30}{2} = \frac{30 \times 29}{2} = 435$$ 4. **Calculate ways to pick 2 red balls:** $$\binom{12}{2} = \frac{12 \times 11}{2} = 66$$ 5. **Calculate ways to pick 2 blue balls:** $$\binom{8}{2} = \frac{8 \times 7}{2} = 28$$ 6. **Calculate ways to pick 2 green balls:** $$\binom{10}{2} = \frac{10 \times 9}{2} = 45$$ 7. **Sum of favorable outcomes:** $$66 + 28 + 45 = 139$$ 8. **Probability both balls are the same color:** $$\frac{139}{435}$$ **Final answer:** B) 139/435