A box contains 4 green, 5 red, and 6 blue balls. Two balls are drawn successively without replacement. Find the probability that both balls drawn are of the same colour.
Answer
31/105
The correct answer is 31/105 — Sum = (6+10+15)/105 = 31/105. Hence the required probability is 31/105.
Step-by-step solution
- Total balls = 4+5+6 = 15.
- Probability that both are green: (4/15) * (3/14) = 12/210 = 2/35.
- Probability that both are red: (5/15) * (4/14) = 20/210 = 2/21.
- Probability that both are blue: (6/15) * (5/14) = 30/210 = 1/7.
- Since the colour cases are mutually exclusive, add the three probabilities: 2/35 + 2/21 + 1/7.
- Convert to a common denominator 105: 2/35 = 6/105, 2/21 = 10/105, 1/7 = 15/105.
- Sum = (6+10+15)/105 = 31/105. Hence the required probability is 31/105.
Common mistake: Forgetting to reduce the total number of balls after the first draw and adding probabilities instead of multiplying
Concept tested: Dependent events (without replacement)
Published · How this solution was prepared and checked
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