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 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?
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For probability with multiple groups, sum the favorable outcomes for each group and divide by total combinations.
Updated On: Aug 27, 2025
- \( \frac{19}{66} \)
- \( \frac{17}{66} \)
- \( \frac{15}{66} \)
\( \frac{13}{66} \)
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The Correct Option is A
Solution and Explanation
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 \( \frac{19}{66} \).
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