AMC 8 2013 Problem 14

AMC8 2013 年第 14 题

概率★★★☆☆

Abe holds 1 green and 1 red jelly bean in his hand. Bob holds 1 green, 1 yellow, and 2 red jelly beans in his hand. Each randomly picks a jelly bean to show the other. What is the probability that the colors match?

Abe 手里拿着一颗绿色的和一颗红色的果冻豆。Bob 手里拿着一颗绿色的、一颗黄色的和两颗红色的果冻豆。每个人随机挑选一个果冻豆给对方看。那么这两颗果冻豆颜色匹配的概率是多少？

A. $\frac14$
B. $\frac13$
C. $\frac38$
D. $\frac12$
E. $\frac23$

正确答案 · Correct Answer

解析 · Solution

Solution 1

The favorable responses are either they both show a green bean or they both show a red bean. The probability that both show a green bean is

\displaystyle \frac{1}{2} \cdot \frac{1}{4} = \frac{1}{8}

. The probability that both show a red bean is

\displaystyle \frac{1}{2} \cdot \frac{2}{4} = \frac{1}{4}

. Therefore the probability is

\displaystyle \frac{1}{4} + \frac{1}{8} = \frac{3}{8}

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