View Single Post
  #12  
Old 08-14-2002, 11:25 AM
yal's Avatar
yal yal is offline
Benz-smart
 
Join Date: Oct 1999
Location: New York, Long Island
Posts: 2,707
You guys need to read the New York Times Magazine article (august 11,2002/ section 6) by Lisa Belkin called "The odds of that". Very interesting and thought provoking.....here is a "little" quote from it :-


"When these professors talk, they do so slowly, aware that what they are saying is deeply counterintuitive. No sooner have they finished explaining that the world is huge and that any number of unlikely things are likely to happen than they shift gears and explain that the world is also quite small, which explains an entire other type of coincidence. One relatively simple example of this is ''the birthday problem.'' There are as many as 366 days in a year (accounting for leap years), and so you would have to assemble 367 people in a room to absolutely guarantee that two of them have the same birthday. But how many people would you need in that room to guarantee a 50 percent chance of at least one birthday match?

Intuitively, you assume that the answer should be a relatively large number. And in fact, most people's first guess is 183, half of 366. But the actual answer is 23. In Paulos's book, he explains the math this way: ''[T]he number of ways in which five dates can be chosen (allowing for repetitions) is (365 x 365 x 365 x 365 x 365). Of all these 3655 ways, however, only (365 x 364 x 363 x 362 x 361) are such that no two of the dates are the same; any of the 365 days can be chosen first, any of the remaining 364 can be chosen second and so on. Thus, by dividing this latter product (365 x 364 x 363 x 362 x 361) by 3655, we get the probability that five persons chosen at random will have no birthday in common. Now, if we subtract this probability from 1 (or from 100 percent if we're dealing with percentages), we get the complementary probability that at least two of the five people do have a birthday in common. A similar calculation using 23 rather than 5 yields 1/2, or 50 percent, as the probability that at least 2 of 23 people will have a common birthday.''

Got that?

Using similar math, you can calculate that if you want even odds of finding two people born within one day of each other, you only need 14 people, and if you are looking for birthdays a week apart, the magic number is seven. (Incidentally, if you are looking for an even chance that someone in the room will have your exact birthday, you will need 253 people.) And yet despite numbers like these, we are constantly surprised when we meet a stranger with whom we share a birth date or a hometown or a middle name. We are amazed by the overlap -- and we conveniently ignore the countless things we do not have in common. "
Reply With Quote