Question

一个盒子中有五张卡片，编号为一、二、三、四、五。从盒中随机不放回地选出三张卡片。所选卡片中的最大值为四的概率是多少？

A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected?

$\dfrac{1}{10}$

$\dfrac{1}{5}$

$\dfrac{3}{10}$

$\dfrac{2}{5}$

$\dfrac{1}{2}$

答案：C

知识点：基本概率组合

难度评级：1020

视频讲解：

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文字解答：

选择 $3$ 张卡从 $5$ 张卡中共有 ${5 \choose 3} = 10$ 种方式。如果 $4$ 是最大值，则必须选中四，另外两张从 $\{1, 2, 3\}$ 中选，有 ${3 \choose 2} = 3$ 种方式。因此概率为 $\dfrac{3}{10}$ 。

所以正确答案是 C。

The number of ways to choose $3$ cards from $5$ is ${5 \choose 3} = 10.$ If $4$ is the largest value selected, then the other two cards have to be chosen from $\{1, 2, 3\}.$ There are ${3 \choose 2} = 3$ ways to do this. The probability is then $\dfrac{3}{10}.$

Thus, C is the correct answer.

2017 AMC 8 第 10 题

答案：C

难度评级：1020

视频讲解：

文字解答：

其他年份的第 10 题