Question
A bag contains 5 red , 4 blue , and 3 green
 balls. Two balls are drawn one after another without replacement . What is the probability that both balls are of different colours ?Solution
Total balls = 5 + 4 + 3 = 12 We want: P(both balls are of different colours). P(different colours) = 1 − P(both of same colour) P(both red): = (5/12) × (4/11) = 20/132 P(both blue): = (4/12) × (3/11) = 12/132 P(both green): = (3/12) × (2/11) = 6/132 P(both same colour) = (20 + 12 + 6) / 132 = 38 / 132 = 19 / 66 Therefore, P(different colours) = 1 − 19/66 = (66/66 − 19/66) = 47/66
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