Question

每个转盘都被平均分成 $3$ 部分。转动两个转盘，把得到的两个数相乘。乘积为偶数的概率是多少？

Each spinner is divided into $3$ equal parts. The results obtained from spinning the two spinners 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

小提示：

乘积只有在两个数都是奇数时才是奇数；除此以外都是偶数

A product is even unless both spun numbers are odd

大提示：

先求奇数乘积的概率，也就是奇数乘奇数，再用 $1$ 减去它

Find the probability of an odd product (odd times odd), then subtract from $1$

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

小提示：

大提示：

解答：

其他年份的第 22 题