If 12 dice are thrown at a time,then the prob | vedclass

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(C) For a single die,the possible outcomes are $\{1, 2, 3, 4, 5, 6\}$.Multiples of $3$ on a die are $\{3, 6\}$.The probability of getting a multiple o

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$\left(\frac{2}{3}\right)^{12}$

Vedclass · Answer

(C) For a single die,the possible outcomes are $\{1, 2, 3, 4, 5, 6\}$.Multiples of $3$ on a die are $\{3, 6\}$.The probability of getting a multiple of $3$ on one die is $P(M) = \frac{2}{6} = \frac{1}{3}$.The probability of $NOT$ getting a multiple of $3$ on one die is $P(M') = 1 - \frac{1}{3} = \frac{2}{3}$.Since $12$ dice are thrown independently,the probability that a multiple of $3$ does not appear on any of the $12$ dice is $\left(\frac{2}{3}\right)^{12}$.

If $12$ dice are thrown at a time,then the probability that a multiple of $3$ does not appear on any dice is

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