Question

两个盒子中各有三枚编号为 $1$ 、 $2$ 、 $3$ 的筹码。从每个盒子中随机取出一枚筹码，并将两枚筹码上的数字相乘。乘积为偶数的概率是多少？

Each of two boxes contains three chips numbered $1,$ $2,$ $3.$ A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even?

$\dfrac{1}{9}$

$\dfrac{2}{9}$

$\dfrac{4}{9}$

$\dfrac{1}{2}$

$\dfrac{5}{9}$

答案：E

知识点：对立事件概率奇偶性

难度评级：960

小提示：

统计补集，也就是乘积为奇数，可能更容易

It may be easier to count the complement: an odd product.

大提示：

只有当两枚筹码都是奇数时，乘积才是奇数

The product is odd only if both drawn chips are odd.

视频讲解：

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文字解答：

只有当两枚筹码都是奇数时，乘积才是奇数。每个盒子中有两个奇数筹码 $1$ 和 $3$ ，共三个筹码，所以乘积为奇数的概率是 $(\dfrac23)^2=\dfrac49$ 。

乘积为偶数的概率是补集，等于 $1-\dfrac49=\dfrac59$ 。

所以正确答案是 E。

The product is odd only when both chips are odd. Each box has two odd chips, $1$ and $3,$ out of three chips, so the probability of an odd product is $(\dfrac23)^2=\dfrac49.$

The probability of an even product is the complement, $1-\dfrac49=\dfrac59.$

Thus, E is the correct answer.

2015 AMC 8 第 7 题