Single correct option
A bag contains 4 red, 5 blue and 6 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are of the same colour?
- A. 27/105
- B. 29/105
- C. 31/105
- D. 33/105
Show answer and solution
Answer: (C) 31/105
Total ways to draw 2 balls from 15 = ¹⁵C₂ = 105. Favourable ways (both same colour) = ⁴C₂ + ⁵C₂ + ⁶C₂ = 6 + 10 + 15 = 31. Probability = 31/105. Note this cannot be simplified further since 31 is prime and does not divide 105.
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