1992 AMC 8 第 23 题

Question

掷两颗骰子，朝上点数的乘积大于

10

的概率是

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

\dfrac37

\dfrac{17}{36}

\dfrac12

\dfrac58

\dfrac{11}{12}

答案：B

知识点：骰子（概率）系统列举

难度评级：1150

小提示：

6 \times 6 = 36

个等可能结果；数出乘积大于

10

的结果。

There are

6 \times 6 = 36

equally likely outcomes; count those whose product exceeds

10

大提示：

做一个

6 \times 6

的乘法表，并标出所有大于

10

的乘积。

Make a

6 \times 6

multiplication table and mark every product greater than

10

解答：

36

个等可能结果。按第一颗骰子的点数，计算乘积大于

10

的有序数对：若为

2

，有

1

个结果满足，即

2 \times 6

；若为

3

，有

3

个；若为

4

，有

4

个；若为

5

，有

4

个；若为

6

，有

5

个。

有利结果总数为

1 + 3 + 4 + 4 + 5 = 17

，所以概率是

\dfrac{17}{36}

。

所以正确答案是 B。

There are

36

equally likely outcomes. Counting the ordered pairs whose product exceeds

10

: with a first die of

2

there is

1

(namely

2 \times 6

); of

3

, there are

3

; of

4

, there are

4

; of

5

, there are

4

; of

6

, there are

5.

That is

1 + 3 + 4 + 4 + 5 = 17

favorable outcomes, so the probability is

\dfrac{17}{36}.

Thus, the correct answer is B .

1992 AMC 8 第 23 题

答案：B

难度评级：1150

小提示：

大提示：

解答：

其他年份的第 23 题