AMC8 2003

AMC8 2003 · Q12

AMC8 2003 · Q12. It mainly tests Probability (basic), Divisibility & factors.

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?

当一个公平的六面骰子掷在桌面上时，底面看不到。五个可见面上的数字乘积能被 6 整除的概率是多少？

(A) \frac{1}{3} \frac{1}{3}

(B) \frac{1}{2} \frac{1}{2}

(D) \frac{5}{6} \frac{5}{6}

(E) 1 1

Answer

Correct choice: (E)

正确答案：（E）

Solution

If 6 is one of the visible faces, the product will be divisible by 6. If 6 is not visible, the product of the visible faces will be $1 \times 2 \times 3 \times 4 \times 5 = 120$, which is also divisible by 6. Because the product is always divisible by 6, the probability is 1.

如果 6 是可见面之一，则乘积能被 6 整除。如果 6 不可见，则可见面的乘积为 $1 \times 2 \times 3 \times 4 \times 5 = 120$，也同样能被 6 整除。因为乘积总是能被 6 整除，所以概率为 1。

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