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NDA 2 2024 Maths, question 106

Topic: Probability

Q106

A box contains 22 black, 44 yellow and 66 white balls. Three balls are drawn in succession with replacement. What is the probability that all three are of the same colour?

  1. (a) 1/61/6Correct answer
  2. (b) 1/361/36
  3. (c) 1/121/12
  4. (d) 5/125/12

Solution.

Answer: (a) 1/61/6

  1. Replacement makes successive colour probabilities unchanged.
  2. The same-colour possibilities are disjoint, so add their probabilities: (2/12)³+(4/12)³+(6/12)³=1/216+8/216+27/216=36/216=1/6.