Numerical answer
A bag contains 5 red and 7 blue balls. Two balls are drawn at random without replacement. The probability that both balls are of the same colour is p/q in lowest terms. Find p + q.
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Answer: 97
Total ways to choose 2 from 12 balls = C(12,2) = 66. Favourable ways (same colour) = C(5,2) + C(7,2) = 10 + 21 = 31. Probability = 31/66, which is already in lowest terms since 31 is prime and does not divide 66. So p+q = 31+66 = 97.
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