Problem:
Juan rolls a fair regular octahedral die marked with the numbers 1 through 8 . Then Amal rolls a fair six-sided die. What is the probability that the product of the two rolls is a multiple of 3 ?
Answer Choices:
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Solution:
The product will be a multiple of 3 if and only if at least one of the two rolls is a 3 or a 6 . The probability that Juan rolls 3 or 6 is . The probability that Juan does not roll 3 or 6 , but Amal does is . Thus, the probability that the product of the rolls is a multiple of 3 is
The problems on this page are the property of the MAA's American Mathematics Competitions