Question

海滩上有 $50$ 人戴太阳镜， $35$ 人戴帽子。有些人两者都戴。如果从戴帽子的人中随机选一人，此人也戴太阳镜的概率是 $\dfrac{2}{5}$ 。如果改为从戴太阳镜的人中随机选一人，此人也戴帽子的概率是多少？

On a beach $50$ people are wearing sunglasses and $35$ people are wearing caps. Some people are wearing both sunglasses and caps. If one of the people wearing a cap is selected at random, the probability that this person is also wearing sunglasses is $\dfrac{2}{5}.$ If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?

$\displaystyle \dfrac{14}{85}$

$\displaystyle \dfrac{7}{25}$

$\displaystyle \dfrac{2}{5}$

$\displaystyle \dfrac{4}{7}$

$\displaystyle \dfrac{7}{10}$

答案：B

知识点：条件概率

难度评级：1100

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文字解答：

概率为 $\dfrac{2}{5}$ ，表示戴帽子的人中有 $\dfrac{2}{5}$ 也戴太阳镜。

所以两者都戴的人数为 $35 \cdot \dfrac{2}{5} = 14$ 。

从戴太阳镜的五十人中随机选，选到也戴帽子的概率为 $\dfrac{14}{50} = \dfrac{7}{25}$ 。

正确答案是 B。

If the probability is $\dfrac{2}{5},$ that means $\dfrac{2}{5}$ of the people wearing caps are also wearing sunglasses.

This means that $35 \cdot \dfrac{2}{5} = 14$ people are wearing both caps and sunglasses.

The probability of a person wearing sunglasses also wearing a cap is $\dfrac{14}{50} = \dfrac{7}{25}.$

Thus, the correct answer is B.

2019 AMC 8 第 15 题

答案：B

难度评级：1100

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