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# Two fair dice are thrown together. what is the probability that the nu

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Re: Two fair dice are thrown together. what is the probability that the nu [#permalink]
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Given that Two fair dice are thrown together and we need to find what is the probability that the number obtained on one of the dice is a multiple of the number obtained on the other die?

As we are rolling two dice => Number of cases = $$6^2$$ = 36

Lets start writing the possible cases where number of one dice is a multiple of other

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6) [ All cases with 1 in the first roll are possible as all numbers are multiples of 1 ]
(2,1), (2,2), (2,4), (2,6)
(3,1), (3,3), (3,6)
(4,1), (4,2), (4,4)
(5,1), (5,5)
(6,1), (6,2), (6,3), (6,6)

=> 22 cases

=> Probability that the number obtained on one of the dice is a multiple of the number obtained on the other die = $$\frac{22}{36}$$ = $$\frac{11}{18}$$