If three dice are thrown simultaneously, then the probability of getti

1.	If three dice are thrown simultaneously, then the probability of getting a score of 5 is A. \(\frac{5}{216}\) B. \(\frac{1}{6}\)C. \(\frac{1}{36}\) D. none of these
Answer» As 3 dice are thrown so there are 6×6×6 = 216 possibilities. Let E denote the event of getting a total score of 5. {(1,1,3),(1,2,2)} As (1,1,3) can be arranged in \(\frac{3!}{2!}\) ways = 3 and (1,2,2) can be arranged in \(\frac{3!}{2!}\) ways = 3 ∴ n(E) = 6 Hence, P(E) = \(\frac{6}{36}\) = \(\frac{1}{6}\) As our answer matches only with option (b) ∴ Option (b) is the only correct choice.

If three dice are thrown simultaneously, then the probability of getting a score of 5 is A. \(\frac{5}{216}\) B. \(\frac{1}{6}\)C. \(\frac{1}{36}\) D. none of these

Answer»

As 3 dice are thrown so there are 6×6×6 = 216 possibilities.

Let E denote the event of getting a total score of 5.

{(1,1,3),(1,2,2)}

As (1,1,3) can be arranged in \(\frac{3!}{2!}\) ways = 3

and (1,2,2) can be arranged in \(\frac{3!}{2!}\) ways = 3

∴ n(E) = 6

Hence,

P(E) = \(\frac{6}{36}\) = \(\frac{1}{6}\)

As our answer matches only with option (b)

∴ Option (b) is the only correct choice.

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If three dice are thrown simultaneously, then the probability of getting a score of 5 is A. \(\frac{5}{216}\) B. \(\frac{1}{6}\)C. \(\frac{1}{36}\) D. none of these

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