Question

一个转盘被平均分成三部分，分别标着 $1$ 、 $2$ 和 $3$ 。第二个转盘也被平均分成三部分，分别标着 $4$ 、 $5$ 和 $6$ 。两个转盘各转一次，把得到的两个数相乘。乘积为偶数的概率是多少？

One spinner is divided into three equal parts labeled $1,$ $2,$ and $3.$ A second spinner is divided into three equal parts labeled $4,$ $5,$ and $6.$ Each spinner is spun once and the two resulting numbers are multiplied. What is the probability that this product is an even number?

$\dfrac13$

$\dfrac12$

$\dfrac23$

$\dfrac79$

$1$

答案：D

知识点：对立事件概率奇偶性

难度评级：1000

解答：

乘积为奇数当且仅当两个数都是奇数。第一个转盘转到奇数 $1$ 或 $3$ 的概率是 $\dfrac23$ ，第二个转盘转到奇数 $5$ 的概率是 $\dfrac13$ 。

所以乘积为奇数的概率是 $\dfrac23 \times \dfrac13 = \dfrac29$ ，乘积为偶数的概率是 $1 - \dfrac29 = \dfrac79$ 。

所以正确答案是 D。

The product is odd only when both numbers are odd. The first spinner is odd ( $1$ or $3$ ) with probability $\dfrac23,$ and the second is odd ( $5$ ) with probability $\dfrac13.$

So the product is odd with probability $\dfrac23 \times \dfrac13 = \dfrac29,$ and even with probability $1 - \dfrac29 = \dfrac79.$

Thus, the correct answer is D .

1991 AMC 8 第 22 题

答案：D

难度评级：1000

解答：

其他年份的第 22 题