1987 AMC 8 第 25 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。
25.
罐子里有编号 到 的十个球。杰克伸手随机取出一个球。然后吉尔伸手随机取出另一个不同的球。取出的两个球上的数字之和为偶数的概率是多少？
Ten balls numbered to are in a jar. Jack reaches into the jar and randomly removes one of the balls. Then Jill reaches into the jar and randomly removes a different ball. What is the probability that the sum of the two numbers on the balls removed is even?
小提示：
两个数的和为偶数，当且仅当两个数同为奇数或同为偶数
The sum of two numbers is even exactly when both are odd or both are even
大提示：
有 个奇数球和 个偶数球；在全部 对中数出同奇偶性的对数
There are odd and even balls; count the matching-parity pairs out of all pairs
解答：
和为偶数时，两个球同为奇数或同为偶数。全奇的配对有 对，全偶的配对也有 对，共 对有利情况。
总配对数是 ，所以概率是 。
所以正确答案是 A。
The sum is even when both balls are odd or both are even. There are all-odd pairs and all-even pairs, for favorable pairs.
The total number of pairs is so the probability is
Thus, the correct answer is A .
其他年份的第 25 题
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