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Jeff rolls a fair regular octahedral die marked with the numbers 1 through 8. Then Amelie rolls a fair six-sided die. What is the probability that the product of the two rolls is a multiple of 3?

 Oct 29, 2019
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We can make a table:

 

1   2   3   4   5   6   7   8

                                                                                         1  1   2   3   4   5   6   7   8

                                                                                         2  2   4   6   8  10 12 14 16

                                                                                         3  3   6   9  12 15 18 21 24

                                                                                         4  4   8  12 16 20 24 28 32

                                                                                         5  5  10 15 20 25 30 35 40

                                                                                         6  6  12 18 24 30 36 42 48

 

We can see that in the table there are 48 values, and 24 of these are a multiple of three, so the probability that the product of the two rolls is a multiple of 3 is 24/48 = 1/2.

 Oct 30, 2019

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