AMC 8 2007 Problem 21
AMC8 2007 年第 21 题
概率★★★☆☆
Two cards are dealt from a deck of four red cards labeled , , , and four green cards labeled , , , . A winning pair is two of the same color or two of the same letter. What is the probability of drawing a winning pair?
从 4 张标有 A，B，C，D 的红牌和 4 张标有 A，B，C，D 的绿牌中选择 2 张牌。一对获胜的牌是指两张同色的牌或者两张字母一样的牌。那么抽到的 2 张牌是一对获胜的牌的概率是多少？
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
Notice that, no matter which first card you choose, there are exactly 4 cards that either have the same color or letter as it. Since there are 7 cards left to choose from, the probability is frac47. -theepiccarrot7
We can use casework to solve this. Case 1: Same letter After choosing any letter, there are seven cards left, and only one of them will produce a winning pair. Therefore, the probability is . Case 2: Same color After choosing any letter, there are seven cards left. Three of them will make a winning pair, so the probability is . Now that we have the probability for both cases, we can add them: .
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