# Given Information - A box contains **4 red balls**, **5 blue balls**, and **6 green balls**. - Two balls are drawn **randomly without replacement**. # What Have to Find - The probability that **both balls drawn are of the same color** (event \( A \)). # Definition or Concept Used - **Probability of an event** = (Number of favorable outcomes) / (Total number of possible outcomes). - When drawing without replacement, use combinations to count outcomes: The number of ways to choose \( r \) objects from \( n \) is \( \binom{n}{r} \). # Step-by-Step Solution Total number of balls = 4 (red) + 5 (blue) + 6 (green) = 15 Total ways to choose 2 balls from 15: \[ \binom{15}{2} = \frac{15 \times 14}{2} = 105 \] Number of ways to choose 2 balls of the same color: - Both red: \( \binom{4}{2} = 6 \) - Both blue: \( \binom{5}{2} = 10 \) - Both green: \( \binom{6}{2} = 15 \) Total favorable outcomes = 6 + 10 + 15 = 31 Probability of event \( A \): \[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{31}{105} \] # Summary The probability that both balls drawn are of the same color is **\(\frac{31}{105}\)**.