2019 AMC 8 第 18 题

先试着解答 2019 AMC 8 第 18 题,然后核对你的答案与视频与精心整理的解答,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 2019 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。

18.

两个公平骰子的各面都标有 11、22、33、55、77 和 88。掷这两个骰子时,它们点数之和为偶数的概率是多少?
The faces of each of two fair dice are numbered 1,1, 2,2, 3,3, 5,5, 7,7, and 8.8. When the two dice are tossed, what is the probability that their sum will be an even number?
49\displaystyle \dfrac{4}{9}
12\displaystyle \dfrac{1}{2}
59\displaystyle \dfrac{5}{9}
35\displaystyle \dfrac{3}{5}
23\displaystyle \dfrac{2}{3}
答案:C
知识点:骰子(概率)奇偶性
小提示:
和为偶数表示两个骰子的奇偶性相同
An even sum means both dice have the same parity
大提示:
每个骰子有 22 个偶数面和 44 个奇数面
Each die has 22 even faces and 44 odd faces
视频讲解:
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文字解答:
和为偶数有两种情况:两个都是偶数,或两个都是奇数。
单个骰子掷出偶数的概率为 26=13\dfrac{2}{6} = \dfrac{1}{3},掷出奇数的概率为 46=23\dfrac{4}{6} = \dfrac{2}{3}。
因此所求概率为 13⋅13+23⋅23=59。 \dfrac{1}{3} \cdot \dfrac{1}{3} + \dfrac{2}{3} \cdot \dfrac{2}{3} = \dfrac{5}{9}\text{。}
正确答案是 C。
The only two ways that the sum can be even is if both rolls are even or both are odd.
The probability that a roll is even is 26=13,\dfrac{2}{6} = \dfrac{1}{3}, and the probability that it is odd is 46=23.\dfrac{4}{6} = \dfrac{2}{3}.
Therefore, the desired probability is 13⋅13+23⋅23=59. \dfrac{1}{3} \cdot \dfrac{1}{3} + \dfrac{2}{3} \cdot \dfrac{2}{3} = \dfrac{5}{9}.
Thus, the correct answer is C.
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