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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Probability

NDA 2023 · Mathematics · Probability

Three dice are thrown. What is the probability that each face shows...

Three dice are thrown. What is the probability that each face shows only multiples of 3 ?

Options

  1. A19\frac{1}{9}
  2. B118\frac{1}{18}
  3. C127\frac{1}{27}
  4. D13\frac{1}{3}

Correct answer

C. 127\frac{1}{27}

Step-by-step solution

On throw of 3 dice, Number of possible outcomes =63=216=6^3=216 Favourable outcomes ={(3,3,3),(3,3,6),(3,6,3),(6,3,3),(3,6,6)(6,3,6),(6,6,3),(6,6,6)}\begin{aligned} &=\{(3,3,3),(3,3,6),(3,6,3),(6,3,3),(3,6,6) \\ &(6,3,6),(6,6,3),(6,6,6)\}\end{aligned} Probability = Number of favourable outcomes  Number of total outcomes =8216=127=\frac{\text{ Number of favourable outcomes }}{\text{ Number of total outcomes }}=\frac{8}{216}=\frac{1}{27}
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