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[img]ct_4image002[/img]The figure above shows a rectangular play area in which
[img]ct_4image002[/img]The figure above shows a rectangular play area in which
游客
2025-02-24
10
管理
问题
The figure above shows a rectangular play area in which one child stands at B while another child runs back and forth along the entire side AD. If the running child is in a position randomly located along side AD at a given time, what is the probability that the two children are at most 50 feet apart at that time?
选项
A、1/5
B、2/5
C、3/5
D、4/5
E、1
答案
D
解析
左面图形表示一个长方形的娱乐区,有一个小孩站在B点,同时另一个小孩在A和D之间来回跑动。若跑步的小孩在AD边上的位置在任一时刻都是随机的,两个小孩最多相距50英尺的概率(probability)是多少?
解:本题的正确答案是(D)。根据题意可知,两个孩子的位置及点A在任意时刻都可构成一个直角三角形,直角三角形的斜边长就是两个孩子之间的距离,两个孩子的距离不超过50英尺,即直角三角形的斜边不超过50英尺,AB=30英尺,根据勾股定理可知,跑步的小孩离A点的距离应不超过40英尺时,才能使他们之间的距离不超过50英尺。而跑步的小孩在AD上的位置是随机的,因此两个小孩最多相距50英尺的概率是40/50=4/5
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