Question

Diana 和 Apollo 各掷一颗标准骰子，随机得到 $1$ 到 $6$ 中的一个数。Diana 的数大于 Apollo 的数的概率是多少？

Diana and Apollo each roll a standard die obtaining a number at random from $1$ to $6.$ What is the probability that Diana's number is larger than Apollo's number?

$\dfrac13$

$\dfrac{5}{12}$

$\dfrac49$

$\dfrac{17}{36}$

$\dfrac12$

答案：B

知识点：骰子（概率）对称性

难度评级：1120

解答：

共有 $6 \times 6 = 36$ 个等可能结果，其中 $6$ 个是平局，剩下 $30$ 个结果两数不同。

由对称性，Diana 的数较大的情况正好是其中一半，即 $15$ 个。所以概率为 $\dfrac{15}{36} = \dfrac{5}{12}$ 。

所以正确答案是 B。

There are $6 \times 6 = 36$ equally likely outcomes, of which $6$ are ties, leaving $30$ outcomes with different numbers.

By symmetry, Diana is larger in exactly half of those, or $15,$ so the probability is $\dfrac{15}{36} = \dfrac{5}{12}.$

Thus, the correct answer is B .

1995 AMC 8 第 20 题

答案：B

难度评级：1120

解答：

其他年份的第 20 题