Question

A bag contains 3 red, 4 white, and 5 blue balls. Two balls are drawn at random. What is the probability that both are of the same color?

• A. \( \frac{19}{66} \)
• B. \( \frac{17}{66} \)
• C. \( \frac{15}{66} \)
• D. \( \frac{13}{66} \)

Hint:

For probability with multiple groups, sum the favorable outcomes for each group and divide by total combinations.

Answer 1

The Correct Option is A

Total balls = \( 3 + 4 + 5 = 12 \). Total ways to draw 2 balls = \( \binom{12}{2} = 66 \). 
Same color: 
- Red: \( \binom{3}{2} = 3 \) 
- White: \( \binom{4}{2} = 6 \) 
- Blue: \( \binom{5}{2} = 10 \) 
Total favorable = \( 3 + 6 + 10 = 19 \). 
Probability = \( \frac{19}{66} \). 
Thus, the answer is \( \frac{19}{66} \).