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Alice rolls a fair six sided die, and Bob rolls a fair twenty sided die. What is the probability that the product of the numbers they roll is a multiple of 5?

 Oct 13, 2022
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(1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 12, 12, 12, 12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 18, 19, 20, 20, 20, 20, 21, 22, 24, 24, 24, 24, 25, 26, 27, 28, 28, 30, 30, 30, 30, 32, 32, 33, 34, 35, 36, 36, 36, 36, 38, 39, 40, 40, 40, 42, 42, 44, 45, 45, 48, 48, 48, 50, 51, 52, 54, 54, 55, 56, 57, 60, 60, 60, 60, 64, 65, 66, 68, 70, 72, 72, 75, 76, 78, 80, 80, 84, 85, 90, 90, 95, 96, 100, 102, 108, 114, 120)>>Total = 120 possible products

 

(5, 5, 10, 10, 10, 15, 15, 15, 20, 20, 20, 20, 25, 30, 30, 30, 30, 35, 40, 40, 40, 45, 45, 50, 55, 60, 60, 60, 60, 65, 70, 75, 80, 80, 85, 90, 90, 95, 100, 120) >>Total = 40 products that are multiples of 5

 

Therefore, the probability is: 40 / 120 ==1 / 3

 Oct 13, 2022

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