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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Probability

NDA 2022 · Mathematics · Probability

Three fair dice are tossed once. What is the probability that they...

Three fair dice are tossed once. What is the probability that they show different numbers that are in APA P ?

Options

  1. A112\frac{1}{12}
  2. B118\frac{1}{18}
  3. C136\frac{1}{36}
  4. D172\frac{1}{72}

Correct answer

B. 118\frac{1}{18}

Step-by-step solution

n(s)=6×6×6n(s)=6 \times 6 \times 6 Different numbers that are in AP. (1,2,3),(2,3,4),(3,4,5),(4,5,6),(1,3,5),(2,4,6),(3,2,1),(4,3,2),(5,4,3),(6,5,4),(5,3,1),(6,4,2)n(E)=12P(E)=126×6×6=118\begin{aligned} & (1,2,3),(2,3,4),(3,4,5),(4,5,6),(1,3,5),(2,4, \\ & 6),(3,2,1),(4,3,2),(5,4,3),(6,5,4),(5,3,1),(6, \\ & 4,2) \\ & n(E)=12 \\ & P(E)=\frac{12}{6 \times 6 \times 6}=\frac{1}{18} \end{aligned}
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