Question

转盘 $A$ 和 $B$ 被旋转。在每个转盘上，指针落在每个数字上的可能性相同。两个转盘数字的乘积为偶数的概率是多少？

Spinners $A$ and $B$ are spun. On each spinner, the arrow is equally likely to land on each number. What is the probability that the product of the two spinners' numbers is even?

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{1}{2}$

$\dfrac{2}{3}$

$\dfrac{3}{4}$

答案：D

知识点：基本概率对立事件概率奇偶性

难度评级：1290

解答：

要使乘积为偶数，至少一个转盘必须落在偶数上。

使用补集计数，计算两个转盘都落在奇数上的概率。

这个概率为 $\dfrac{1}{2} \cdot \dfrac{2}{3} = \dfrac{1}{3}.$

因此至少一个为偶数的概率为 $1 - \dfrac{1}{3} = \dfrac{2}{3}.$

所以正确答案是 D。

For the product to be even, then at least one of the spinners must land on an even number.

We can use complementary counting and calculate the probability of both spinners landing on odds.

This happens with a probability of $\dfrac{1}{2} \cdot \dfrac{2}{3} = \dfrac{1}{3}.$

Then the probability of landing on at least one even is $1 - \dfrac{1}{3} = \dfrac{2}{3}.$

Thus, D is the correct answer.

2004 AMC 8 第 21 题

答案：D

难度评级：1290

解答：

其他年份的第 21 题