2001 AMC 8 第 18 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
18.
掷两个骰子。两个点数的乘积是 的倍数的概率是多少？
Two dice are thrown. What is the probability that the product of the two numbers is a multiple of
小提示：
乘积是 的倍数，当且仅当至少一个骰子掷出
The product is a multiple of exactly when a die shows
大提示：
数没有骰子掷出 的情况更容易
It is easier to count no die showing
解答：
乘积是 的倍数的唯一方法是至少一个骰子掷出 。
用补集计数。两个骰子都不掷出 的概率是
因此至少一个骰子掷出 的概率为
所以正确答案是 D。
The only way for the product to be a multiple of is if at least one of the rolls is
We can do complementary counting. The probability that neither rolls is a is
Therefore, the probability that at least one roll is a is
Thus, D is the correct answer.
其他年份的第 18 题
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