AMC8 1992

AMC8 1992 · Q23

AMC8 1992 · Q23. It mainly tests Probability (basic).

If two dice are tossed, the probability that the product of the numbers showing on the tops of the dice is greater than 10 is

抛掷两个骰子，两个骰子顶面数字之积大于10的概率是

(A) \frac{3}{7} \frac{3}{7}

(B) \frac{17}{36} \frac{17}{36}

(D) \frac{5}{8} \frac{5}{8}

(E) \frac{11}{12} \frac{11}{12}

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Make a table and fill the products greater than 10. \[ \begin{array}{c|cccccc} \times & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1: & 1 & 2 & 3 & 4 & 5 & 6 \\ 2: & 2 & 4 & 6 & 8 & 10 & 12 \\ 3: & 3 & 6 & 9 & 12 & 15 & 18 \\ 4: & 4 & 8 & 12 & 16 & 20 & 24 \\ 5: & 5 & 10 & 15 & 20 & 25 & 30 \\ 6: & 6 & 12 & 18 & 24 & 30 & 36 \\ \end{array} \] Since there are 17 such products out of a possible 36 products, the probability is \[ \frac{17}{36} \].

答案 (B)：制表并填入大于10的乘积。 \[ \begin{array}{c|cccccc} \times & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1: & 1 & 2 & 3 & 4 & 5 & 6 \\ 2: & 2 & 4 & 6 & 8 & 10 & 12 \\ 3: & 3 & 6 & 9 & 12 & 15 & 18 \\ 4: & 4 & 8 & 12 & 16 & 20 & 24 \\ 5: & 5 & 10 & 15 & 20 & 25 & 30 \\ 6: & 6 & 12 & 18 & 24 & 30 & 36 \\ \end{array} \] 36个乘积中有17个大于10，因此概率为 \[ \frac{17}{36} \]。

Topics

CP.006 Probability (basic)