2019 AMC 8 第 15 题

先试着解答 2019 AMC 8 第 15 题,然后核对你的答案与视频与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2019 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

15.

海滩上有 5050 人戴太阳镜,3535 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 25\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 5050 people are wearing sunglasses and 3535 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 25.\dfrac{2}{5}. If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?
1485\displaystyle \dfrac{14}{85}
725\displaystyle \dfrac{7}{25}
25\displaystyle \dfrac{2}{5}
47\displaystyle \dfrac{4}{7}
710\displaystyle \dfrac{7}{10}
答案:B
知识点:条件概率
小提示:
用戴帽子的人群先求两者都戴的人数
Use the cap group to find the number wearing both
大提示:
再把同一个交集人数除以戴太阳镜的人数
Then divide that same overlap by the number wearing sunglasses
视频讲解:
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文字解答:
概率为 25\dfrac{2}{5},表示戴帽子的人中有 25\dfrac{2}{5} 也戴太阳镜。
所以两者都戴的人数为 35⋅25=1435 \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 1450=725\dfrac{14}{50} = \dfrac{7}{25}。
正确答案是 B。
If the probability is 25,\dfrac{2}{5}, that means 25\dfrac{2}{5} of the people wearing caps are also wearing sunglasses.
This means that 35⋅25=1435 \cdot \dfrac{2}{5} = 14 people are wearing both caps and sunglasses.
The probability of a person wearing sunglasses also wearing a cap is 1450=725.\dfrac{14}{50} = \dfrac{7}{25}.
Thus, the correct answer is B.
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