AMC 8 2017 Problem 10

AMC8 2017 年第 10 题

概率★★☆☆☆

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?

一个盒子装了标有 1,2,3,4,5 的 5 张卡片。从中不放回的随机选择 3 张卡片，问 4 是选择的最大的数的概率是多少？

A. $\displaystyle \frac{1}{10}$
B. $\displaystyle \frac{1}{5}$
C. $\displaystyle \frac{3}{10}$
D. $\displaystyle \frac{2}{5}$
E. $\displaystyle \frac{1}{2}$

正确答案 · Correct Answer

解析 · Solution

Solution 1

There are 10 10 possible equally likely outcomes: The three highlighted outcomes have 4 4 as the largest value selected. Hence the probability is 3 10 10 3 . OR OR There are 10 10 ways to select 3 3 cards without replacement from a box of 5 5 cards. If the largest value selected is 4 4, then the remaining two cards can be selected from the cards 1, 2 1,2, and 3 3 in 3 3 ways. So, the probability that 4 4 is the largest value selected is 3 10 10 3 . Answer: 𝐶 C .

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