Question

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

Two different numbers are selected at random from $\{1, 2, 3, 4, 5\}$ and multiplied together. What is the probability that the product is even?

$\ 0.2$

$\ 0.4$

$\ 0.5$

$\ 0.7$

$\ 0.8$

答案：D

知识点：基本概率补集计数奇偶性

难度评级：960

解答：

乘积为奇数当且仅当两个数都是奇数。有 $\binom 32=3$ 种奇数对，总共有 $\binom 52=10$ 种数对。因此乘积为奇数的概率为 $\frac 3{10} = 0.3$ ，乘积为偶数的概率为 $1-0.3=0.7$ 。

所以正确答案是 D。

The product is odd if and only if both numbers are odd. There are $\binom 32=3$ ways to do this out of a possible $\binom 52=10$ ways. This makes the probability of it being odd equal to $\frac 3{10} = 0.3.$ This means the probability it is even is $1-0.3=0.7.$

Thus, the correct answer is D .

2016 AMC 10B 第 12 题

答案：D

难度评级：960

解答：

其他年份的第 12 题