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      Question

      A dice is rolled six times. What is the probability that

      a six appears on the sixth roll for the second time in 6 rolls?
      A 1/15 Correct Answer Incorrect Answer
      B 5/36 Correct Answer Incorrect Answer
      C 1/12 Correct Answer Incorrect Answer
      D 1/9 Correct Answer Incorrect Answer
      E 7/36 Correct Answer Incorrect Answer

      Solution

      Six can appear in these ways:
      6XXXX6, X6XXX6, XX6XX6, XXX6X6 and XXXX66
      Probability that a six appears on the sixth roll for the second time in 6 rolls
      = (1/6)*(1/6) + (1/6)*(1/6) + (1/6)*(1/6) + (1/6)*(1/6) + (1/6)*(1/6) = 5/36

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