Question

从集合中随机选出两个不同的数并相乘。乘积为 $0$ 的概率是多少？ $\{ - 2, -1, 0, 3, 4, 5\}$

Two different numbers are randomly selected from the set $\{ - 2, -1, 0, 3, 4, 5\}$ and multiplied together. What is the probability that the product is $0?$

$\dfrac{1}{6}$

$\dfrac{1}{5}$

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{1}{2}$

答案：D

知识点：基本概率数对计数

难度评级：1020

视频讲解：

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文字解答：

乘积为 $0$ 的唯一方式是所选两个数中有一个是 $0$ 如果第一个数选 $\binom62=15$ ，那么第二个数有 $5$ 种选择。 $\dfrac5{15}=\dfrac13$ 。

同样，第二个数选时也有种选择。因此共有个有序数对，其乘积为总有序数对数为，所以概率为所以正确答案是 D。

There are $\binom62=15$ ways to select two different numbers. A product is $0$ exactly when one selected number is $0$ , and there are $5$ choices for the other number. Thus the probability is $\dfrac5{15}=\dfrac13.$

Thus, D is the correct answer.

2016 AMC 8 第 13 题

答案：D

难度评级：1020

视频讲解：

文字解答：

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