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      Question

      A box contains 5 red balls, 4 blue balls and 3 green

      balls. Two balls are drawn one after the other without replacement. What is the probability that both balls are of different colours?
      A 33/75 Correct Answer Incorrect Answer
      B 47/66 Correct Answer Incorrect Answer
      C 55/23 Correct Answer Incorrect Answer
      D 19/10 Correct Answer Incorrect Answer

      Solution

      Total balls = 5 + 4 + 3 = 12 Total ways to draw 2 balls = C(12, 2) = 66 Total ways to draw 2 balls of the same colour: Both red = C(5, 2) = 10 Both blue = C(4, 2) = 6 Both green = C(3, 2) = 3 Total same-colour ways = 10 + 6 + 3 = 19 Ways of different colours = Total ways − Same-colour ways = 66 − 19 = 47 Probability = 47/66

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