Question

当一个公平的六面骰子被掷到桌面上时，底面看不见。可见的五个面上的数字乘积能被 $6$ 整除的概率是多少？

When a fair six-sided die is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the numbers on the five faces that can be seen is divisible by $6$ ?

$\frac 13$

$\frac 12$

$\frac 23$

$\frac 56$

$1$

答案：E

知识点：基本概率整除性

难度评级：1120

解答：

如果数字 $6$ 的面可见，那么可见数字的乘积能被 $6$ 整除。

如果数字 $6$ 在底面，那么可见面仍包含 $2$ 和 $3$ ，所以它们的乘积仍能被 $6$ 整除。

每种可能的掷骰结果都满足条件，所以概率为 $1$ 。

所以正确答案是 E。

If the face numbered $6$ is visible, then the visible product is divisible by $6$ .

If the face numbered $6$ is on the bottom, then the visible faces include both $2$ and $3$ , so their product is still divisible by $6$ .

Every possible toss works, so the probability is $1$ .

Thus, E is the correct answer.

2003 AMC 8 第 12 题

答案：E

难度评级：1120

解答：

其他年份的第 12 题