笨手笨脚的化学家
The Clumsy Chemist
题目详情
实验室里有若干根细长的 9 英寸玻璃棒，每根一端标有蓝点，另一端标有红点。实验员绊倒后把它们摔在混凝土地面上，许多都断成了三段。对于这些断成三段的玻璃棒，带蓝点那一段的平均长度是多少？
In a laboratory, each of a handful of thin 9-inch glass rods had one tip marked with a blue dot and the other with a red. When the laboratory assistant tripped and dropped them onto the concrete floor, many broke into three pieces. For these, what was the average length of the fragment with the blue dot?
解析
如果把两处断点看作在玻璃棒上随机出现，那么三段长度在对称性下具有相同的期望值：带蓝点的一段、中间一段和带红点的一段的平均长度相同。三段总长为 9 英寸，所以带蓝点那段的平均长度是 。
Original Explanation
Assuming these rods broke at random, the principle of symmetry says that each fragment-blue-dotted, middle, and red-dotted segment-would have the same distribution and the same mean. Since the means have to add to 9 inches, the blue-dotted segments average about 3 inches.