Question

A bag contains 4 red balls, 3 blue balls, and 2 green balls. Two balls are picked at random. What is the probability that both balls are of the same color?

• A. \( \frac{1}{6} \)
• B. \( \frac{2}{9} \)
• C. \( \frac{4}{9} \)
• D. \( \frac{5}{18} \)

Hint:

To calculate probabilities involving combinations, first find the total number of possible outcomes, then the number of favorable outcomes.

Answer 1

The Correct Option is D

The total number of ways to choose 2 balls from 9 (4 red, 3 blue, and 2 green) is \( \binom{9}{2} = 36 \). The favorable outcomes are selecting 2 red balls, 2 blue balls, or 2 green balls: - For red: \( \binom{4}{2} = 6 \) - For blue: \( \binom{3}{2} = 3 \) - For green: \( \binom{2}{2} = 1 \) Thus, the total favorable outcomes are \( 6 + 3 + 1 = 10 \). Therefore, the probability is \( \frac{10}{36} = \frac{5}{18} \).