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017概率中等数值题medium

Product Divisibility in a Token Draw

题目

An urn holds 6 tokens labeled 1,2,3,4,5,61, 2, 3, 4, 5, 6. Two tokens are drawn sequentially *with replacement* (order matters). Construct the sample space and find P(the product of the two drawn numbers is a multiple of 6 but not a multiple of 12)P(\text{the product of the two drawn numbers is a multiple of } 6 \text{ but not a multiple of } 12).

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