AMC8 2001

AMC8 2001 · Q18

AMC8 2001 · Q18. It mainly tests Probability (basic), Divisibility & factors.

Two dice are thrown. What is the probability that the product of the two numbers is a multiple of 5?

掷两个骰子。两个数字之积是5的倍数的概率是多少？

(A) $\frac{1}{36}$ $\frac{1}{36}$

(B) $\frac{1}{18}$ $\frac{1}{18}$

(D) $\frac{11}{36}$ $\frac{11}{36}$

(E) $\frac{1}{3}$ $\frac{1}{3}$

Answer

Correct choice: (D)

正确答案：（D）

Solution

(D) There would be $6 \times 6 = 36$ entries in the table if it were complete, but only the 11 entries that are multiples of 5 are shown. The probability of getting a multiple of 5 is $11/36$. \[ \begin{array}{c|cccccc} \times & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & & & & & 5 & \\ 2 & & & & & 10 & \\ 3 & & & & & 15 & \\ 4 & & & & & 20 & \\ 5 & 5 & 10 & 15 & 20 & 25 & 30 \\ 6 & & & & & 30 & \\ \end{array} \]

(D) 如果这个表格是完整的，那么应有 $6 \times 6 = 36$ 个条目，但这里只显示了 11 个是 5 的倍数的条目。得到 5 的倍数的概率是 $11/36$。 \[ \begin{array}{c|cccccc} \times & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & & & & & 5 & \\ 2 & & & & & 10 & \\ 3 & & & & & 15 & \\ 4 & & & & & 20 & \\ 5 & 5 & 10 & 15 & 20 & 25 & 30 \\ 6 & & & & & 30 & \\ \end{array} \]

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