AMC8 2007

AMC8 2007 · Q21

AMC8 2007 · Q21. It mainly tests Basic counting (rules of product/sum), Probability (basic).

Two cards are dealt from a deck of four red cards labeled A, B, C, D and four green cards labeled A, B, C, D. A winning pair is two of the same color or two of the same letter. What is the probability of drawing a winning pair?

从一副牌中抽出两张牌，这副牌有四张标有A、B、C、D的红牌和四张标有A、B、C、D的绿牌。获胜对子是两张相同颜色或两张相同字母的牌。抽出获胜对子的概率是多少？

(A) $\frac{2}{7}$ $\frac{2}{7}$

(B) $\frac{3}{8}$ $\frac{3}{8}$

(D) $\frac{4}{7}$ $\frac{4}{7}$

(E) $\frac{5}{8}$ $\frac{5}{8}$

Answer

Correct choice: (D)

正确答案：（D）

Solution

(D) After the first card is dealt, there are seven left. The three cards with the same color as the initial card are winners and so is the card with the same letter but a different color. That means four of the remaining seven cards form winning pairs with the first card, so the probability of winning is $\frac{4}{7}$.

（D）发出第一张牌后，还剩下七张牌。与初始牌颜色相同的三张牌都算赢，另外那张字母相同但颜色不同的牌也算赢。这意味着剩下的七张牌中有四张与第一张牌组成获胜配对，因此获胜的概率为 $\frac{4}{7}$。

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