AMC8 2019

AMC8 2019 · Q15

AMC8 2019 · Q15. It mainly tests Probability (basic), Conditional probability (basic).

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 $\frac{2}{5}$. If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?

海滩上有$50$人戴着太阳镜，$35$人戴着帽子。有些人同时戴着太阳镜和帽子。如果从戴帽子的人中随机选一人，该人同时戴太阳镜的概率是$\frac{2}{5}$。如果改从戴太阳镜的人中随机选一人，该人同时戴帽子的概率是多少？

(A) \frac{14}{85} \frac{14}{85}

(B) \frac{7}{25} \frac{7}{25}

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

(E) \frac{7}{10} \frac{7}{10}

Answer

Correct choice: (B)

正确答案：（B）

Solution

The number of people wearing caps and sunglasses is $\frac{2}{5}\cdot35=14$. So then, 14 people out of the 50 people wearing sunglasses also have caps. $\frac{14}{50}=\boxed{\textbf{(B)}\frac{7}{25}}$

同时戴帽子和太阳镜的人数是$\frac{2}{5}\cdot35=14$。因此，在$50$名戴太阳镜的人中，有$14$人同时戴帽子。 $\frac{14}{50}=\boxed{\textbf{(B)}\frac{7}{25}}$

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