Question

右图中的两个转盘各转一次，并把得到的两个数相加。两个数之和为偶数的概率是

The two wheels shown at the right are spun and the two resulting numbers are added. The probability that the sum of the two numbers is even is

$\dfrac{1}{6}$

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{5}{12}$

$\dfrac{4}{9}$

答案：D

知识点：基本概率奇偶性

难度评级：1060

解答：

第一个转盘中， $P(1) = \dfrac14$ ， $P(2) = \dfrac14$ ， $P(3) = \dfrac12$ 。第二个转盘中， $4, 5, 6$ 各自概率为 $\dfrac13$ 。

和为偶数需要两个数同奇偶。两数都为奇数时，第一个数是 $1$ 或 $3$ ，概率为 $\left(\dfrac34\right)$ ；第二个数是 $5$ ，概率为 $\left(\dfrac13\right)$ ，所以概率为 $\dfrac34 \cdot \dfrac13 = \dfrac14$ 。两数都为偶数时，第一个数是 $2$ ，概率为 $\left(\dfrac14\right)$ ；第二个数是 $4$ 或 $6$ ，概率为 $\left(\dfrac23\right)$ ，所以概率为 $\dfrac14 \cdot \dfrac23 = \dfrac16$ 。

总概率是 $\dfrac14 + \dfrac16 = \dfrac{5}{12}$ 。

所以正确答案是 D。

On the first wheel, $P(1) = \dfrac14,$ $P(2) = \dfrac14,$ and $P(3) = \dfrac12.$ On the second wheel, each of $4, 5, 6$ has probability $\dfrac13.$

The sum is even when both numbers are odd or both are even. Both odd: the first is $1$ or $3$ $\left(\dfrac34\right)$ and the second is $5$ $\left(\dfrac13\right),$ giving $\dfrac34 \cdot \dfrac13 = \dfrac14.$ Both even: the first is $2$ $\left(\dfrac14\right)$ and the second is $4$ or $6$ $\left(\dfrac23\right),$ giving $\dfrac14 \cdot \dfrac23 = \dfrac16.$

The total probability is $\dfrac14 + \dfrac16 = \dfrac{5}{12}.$

Thus, the correct answer is D .

1994 AMC 8 第 22 题

答案：D

难度评级：1060

解答：

其他年份的第 22 题