Question

一枚偶数骰子的六个面上只标有偶数，其中 $2$ 、 $4$ 和 $6$ 各出现两次。另一枚奇数骰子的六个面上只标有奇数，其中 $1$ 、 $3$ 和 $5$ 各出现两次。同时掷这两枚骰子，顶面点数之和为 $7$ 的概率是多少？

A pair of six-sided dice are labeled so that one die has only even numbers (two each of $2,$ $4,$ and $6$ ), and the other die has only odd numbers (two each of $1,$ $3,$ and $5$ ). The pair of dice is rolled. What is the probability that the sum of the numbers on the tops of the two dice is $7?$

$\dfrac{1}{6}$

$\dfrac{1}{5}$

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{1}{2}$

答案：D

知识点：骰子（概率）分类讨论

难度评级：960

解答：

和为 $7$ 的点数对是 $(2, 5), (4, 3), \text{ and } (6, 1).$

得到其中任意一个指定点数对的概率为。 $\dfrac{1}{3} \cdot \dfrac{1}{3} = \dfrac{1}{9}$

共有 $3$ 个这样的点数对，所以和为 $7$ 的总概率为 $3 \cdot \dfrac{1}{9} = \dfrac{1}{3}.$

所以正确答案是 D。

The pairs of numbers that sum to $7$ are $(2, 5), (4, 3), \text{ and } (6, 1).$

There is a $\dfrac{1}{3} \cdot \dfrac{1}{3} = \dfrac{1}{9}$ chance that we get any of these pairs.

There are $3$ pairs, which means that the total probability that the rolls sum to $7$ is $3 \cdot \dfrac{1}{9} = \dfrac{1}{3}.$

Thus, D is the correct answer.

2012 AMC 10A 第 9 题

答案：D

难度评级：960

解答：

其他年份的第 9 题