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NDA 2 2024 Maths, question 118

Topic: Probability

Q118

Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?

  1. (a) 5/95/9
  2. (b) 2/32/3
  3. (c) 1/31/3
  4. (d) 1/21/2Correct answer

Solution.

Answer: (d) 1/21/2

  1. Conditioned on all three faces being distinct, there are 6×5×4=120 ordered outcomes.
  2. For an ace, choose its die in 3 ways and the other distinct faces in 5×4 ways, giving 60.
  3. Hence the conditional probability is 60/120=1/2.