何毓琦的个人博客分享 http://blog.sciencenet.cn/u/何毓琦 哈佛(1961-2001) 清华(2001-date)

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Probability and Unusual Events 精选

已有 5202 次阅读 2009-1-2 01:02 |系统分类:科研笔记

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During our California stay this past week, my wife and I by chance met three couples we know from our home town, Boston, on two different days in three different California cities in two restaurants and walking on the street. It turns out these couples were by chance also in California for different reasons. Most people including us consider this set of event to be highly unusual. If one attempts to estimate the probability of this happening, even great mathematician specializing in probability would agree that it must be very very small. And we are right to call this an unusual happening.
However, think about this a bit. Let us denote the three chance meetings my wife and I encountered as happenings A, B, and C. Define a sphere of say diameter of 5 meters around the locations A,B, and C. Since these meeting were in public places, within these spherical volume of space there were other couples who are total strangers to us. Let us single out at least one such couple in each sphere and assign them names CA, CB, and CC. Now ask the question “what probability that at the times of happening A, B, and C, my wife and I  will meet with CA, CB, and CC instead of with our three friendly couples?” Most reasonable people, whether or not having had scientific training, would correctly answer as very small, or even equal to the probability of meeting our three sets of friends from Boston.
But our meetings with three stranger couples happens all the time as we eat in public restaurants and/or walk on the street. We don’t know these stranger couples and we don’t identify them specifically as CA, CB, and CC. Thus, we don’t think them as UNUSUAL when in fact meeting them are just as unusual as meeting our three sets of friends. Put it another way, when we see the daily winning lottery number came out as “1111”, we call this an unusual event; but if the winning number were “2519 (a 4 digit random number)”, we think nothing of it. Even though the fact is that the chance of “1111” happens is just as rare as that of “2519” happens. Because our attachment of special significance to particular events or numbers, we tend to mis-estimate probability quantitatively.
The ignorance of probability by common people can lead to all kinds of misfortunes including taking unnecessary risks, and being cheated by confidence schemes (e.g., the most recent Madoff scandal on Wall Street where even highly intelligent and professional people were taken). I attach a couple of web-pages illustrating this point further
 
 
 
I conclude with the following joke. A person was concerned with terrorists sneaking a bomb abroad an airplane while he is traveling. After advanced field research he found that the probability of there being a bomb on any given flight though small but not small enough for him to feel comfortable. But at the same time he found no record of there are two bombs simultaneously on broad an airplane flight. Thus henceforth he plans to travel in the future always carrying a bomb with him.


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