Question

如图所示的两个转盘各转一次，并各自落在一个编号扇区上。两个扇区中的数字之和为质数的概率是多少？

The two spinners shown are spun once and each lands on one of the numbered sectors. What is the probability that the sum of the numbers in the two sectors is prime?

$\dfrac{1}{2}$

$\dfrac{2}{3}$

$\dfrac{3}{4}$

$\dfrac{7}{9}$

$\dfrac{5}{6}$

答案：D

知识点：基本概率质数

难度评级：1120

解答：

可以求出每种可能结果中两个数字的和。

$\begin{gather*} 1 + 2 = 3 \\ 1 + 4 = 5 \\ 1 + 6 = 7 \\ 3 + 2 = 5 \\ 3 + 4 = 7 \\ 3 + 6 = 9 \\ 5 + 2 = 7 \\ 5 + 4 = 9 \\ 5 + 6 = 11. \end{gather*}$

只有 $2$ 个结果的和不是质数，也就是和为 $9$ 的两种情况。因此和为质数的概率是 $\dfrac{7}{9}$ 。

所以正确答案是 D。

We can find the sum of the two numbers in every possible outcome.

$\begin{gather*} 1 + 2 = 3 \\ 1 + 4 = 5 \\ 1 + 6 = 7 \\ 3 + 2 = 5 \\ 3 + 4 = 7 \\ 3 + 6 = 9 \\ 5 + 2 = 7 \\ 5 + 4 = 9 \\ 5 + 6 = 11. \end{gather*}$

There are only $2$ outcomes where the sum is not prime (the two instances when the sum is $9$ ). Therefore, the probability that the sum is prime is $\dfrac{7}{9}.$

Thus, D is the correct answer.

2009 AMC 8 第 12 题

答案：D

难度评级：1120

解答：

其他年份的第 12 题