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NDA 2025 Maths · Mathematics · Probability · medium

A fair die is rolled twice. The probability that the number on the second roll is strictly greater than the number on the first is

Single correct option

A fair die is rolled twice. The probability that the number on the second roll is strictly greater than the number on the first is
  1. A. 12\dfrac12
  2. B. 518\dfrac5{18}
  3. C. 512\dfrac5{12}
  4. D. 712\dfrac7{12}
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Answer: (C) 512\dfrac5{12}

Of the 3636 equally likely outcomes, 66 have equal numbers, so the remaining 3030 split equally between second greater and first greater, giving 1515 favourable outcomes. Hence P=1536=512P=\frac{15}{36}=\frac5{12}. The value 712\frac7{12} is the probability that the second is greater than or equal to the first, and 12\frac12 forgets the ties.
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Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake