Question

两个公平骰子的各面都标有 $1$ 、 $2$ 、 $3$ 、 $5$ 、 $7$ 和 $8$ 。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 $1,$ $2,$ $3,$ $5,$ $7,$ and $8.$ When the two dice are tossed, what is the probability that their sum will be an even number?

$\displaystyle \dfrac{4}{9}$

$\displaystyle \dfrac{1}{2}$

$\displaystyle \dfrac{5}{9}$

$\displaystyle \dfrac{3}{5}$

$\displaystyle \dfrac{2}{3}$

答案：C

知识点：骰子（概率）奇偶性

难度评级：1100

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 $\dfrac{2}{6} = \dfrac{1}{3}$ ，掷出奇数的概率为 $\dfrac{4}{6} = \dfrac{2}{3}$ 。

因此所求概率为 $\dfrac{1}{3} \cdot \dfrac{1}{3} + \dfrac{2}{3} \cdot \dfrac{2}{3} = \dfrac{5}{9}.$

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 $\dfrac{2}{6} = \dfrac{1}{3},$ and the probability that it is odd is $\dfrac{4}{6} = \dfrac{2}{3}.$

Therefore, the desired probability is $\dfrac{1}{3} \cdot \dfrac{1}{3} + \dfrac{2}{3} \cdot \dfrac{2}{3} = \dfrac{5}{9}.$

Thus, the correct answer is C.

2019 AMC 8 第 18 题

答案：C

难度评级：1100

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文字解答：

其他年份的第 18 题