2004 AMC 8 第 21 题
先试着解答 2004 AMC 8 第 21 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2004 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
21.
转盘 和 被旋转。在每个转盘上，指针落在每个数字上的可能性相同。两个转盘数字的乘积为偶数的概率是多少？
Spinners and are spun. On each spinner, the arrow is equally likely to land on each number. What is the probability that the product of the two spinners’ numbers is even?
小提示：
考虑补事件更容易：乘积为奇数
It is easier to count the complement: an odd product.
大提示：
乘积为奇数要求两个转盘结果都为奇数
An odd product requires both spinner results to be odd.
解答：
要使乘积为偶数，至少一个转盘必须落在偶数上。
使用补集计数，计算两个转盘都落在奇数上的概率。
这个概率为
因此至少一个为偶数的概率为
所以正确答案是 D。
For the product to be even, at least one of the spinners must land on an even number.
We can use complementary counting and calculate the probability of both spinners landing on odds.
This happens with a probability of
Then the probability of landing on at least one even is
Thus, D is the correct answer.
其他年份的第 21 题
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
- 2001 AMC 8
- 2002 AMC 8
- 2003 AMC 8
- 2005 AMC 8
- 2006 AMC 8
- 2007 AMC 8
- 2008 AMC 8
- 2009 AMC 8
- 2010 AMC 8
- 2011 AMC 8
- 2012 AMC 8
- 2013 AMC 8
- 2014 AMC 8
- 2015 AMC 8
- 2016 AMC 8
- 2017 AMC 8
- 2018 AMC 8
- 2019 AMC 8
- 2020 AMC 8
- 2022 AMC 8
- 2023 AMC 8
- 2024 AMC 8
- 2025 AMC 8
- 2026 AMC 8