2. 外语
  3. The figure above shows a rectangular play area in which one child stands at B while another child runs back and forth along the

The figure above shows a rectangular play area in which one child stands at B while another child runs back and forth along the

admin2009-05-19  21
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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