1973 AMC 12 第 23 题

Question

有两张卡片；一张两面都是红色，另一张一面红、一面蓝。两张卡片被选中的概率相同，均为

(\frac{1}{2})

。随机选一张放在桌上。若朝上的一面是红色，则朝下的一面也是红色的概率为

There are two cards; one is red on both sides and the other is red on one side and blue on the other. The cards have the same probability

(\frac{1}{2})

of being chosen, and one is chosen and placed on the table. If the upper side of the card on the table is red, then the probability that the under-side is also red is

\dfrac14

\dfrac13

\dfrac12

\dfrac23

\dfrac34

答案：D

知识点：条件概率基本概率

难度评级：1670

小提示：

按所有可能朝上的红色卡面分别考虑

Condition on the individual card sides that could be showing red

大提示：

共有三个等可能朝上的红色卡面；判断每个卡面的背面颜色

There are three equally likely visible red faces; determine the color behind each

解答：

在朝上一面为红色的结果中，可能朝上的是双红卡的两个红面之一，或红蓝卡的红面。这三个可见的红面等可能出现。前两种情况下背面为红色，第三种情况下背面为蓝色，所以条件概率为

\frac23\text{。}

所以正确答案是 D。

Among outcomes having a red upper side, either of the two red faces of the red-red card or the red face of the red-blue card can be uppermost. These three visible red faces are equally likely. The underside is red in the first two cases and blue in the third, so the conditional probability is

\frac23.

Therefore, the correct answer is D.

1973 AMC 12 第 23 题

答案：D

难度评级：1670

小提示：

大提示：

解答：

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