Numerical answer
A bag contains 5 red balls and 7 blue balls. Three balls are drawn at random without replacement. The probability that all three balls drawn are of the same colour can be written as p/q in its lowest terms. Find p + q.
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Answer: 53
Total ways to choose 3 balls from 12 = C(12,3) = 220. Favourable outcomes (all same colour) = all red: C(5,3) = 10, or all blue: C(7,3) = 35, total = 45. Probability = 45/220 = 9/44 in lowest terms (dividing numerator and denominator by 5). So p = 9, q = 44, and p+q = 53.
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