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      Question

      A bag contains 10 white balls, 4 red balls and 6 black

      balls. Three balls are drawn at random. Find the probability that at least two balls are red.
      A (49/285) Correct Answer Incorrect Answer
      B (5/57) Correct Answer Incorrect Answer
      C (23/114) Correct Answer Incorrect Answer
      D (7/95) Correct Answer Incorrect Answer
      E (13/152) Correct Answer Incorrect Answer

      Solution

      Total = 10 + 4 + 6 = 20
      Required probability = (Two red and one other) + (Three red)

      = 3 Γ— [(4/20) Γ— (3/19) Γ— (16/18)] + (4/20 Γ— 3/19 Γ— 2/18)
      = (576/6840) + (24/6840)
      = (600/6840) = (5/57)

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