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Subject: Re: 和自己同年同月同日出生的人

Author:
Russell Fung

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Date Posted: 13:20:08 12/28/01 Fri
In reply to: mcmen 's message, "和自己同年同月同日出生的人" on 03:17:49 12/27/01 Thu

This is a very interesting question .... at least for those of you with a mathematical mind.

Any time you have more than 21 people, the chance that two of them share the same birthday is greater than 0.5.
For example, my birthday is on 28 Oct, the probability that your birthday is different from mine is 364/365 (ignoring leap year for simplicity). The probability that a third person will have a birthday different from both of ours is 363/365 and so on.
If there are 21 people, the probability that we all have different birthdays is
364/365 * 363/365 * 362/365 * ... *344/365 = 0.5243
If there are 22 people, the probability that we all have different birthdays is
364/365 * 363/365 * 362/365 * ... *343/365 = 0.4927
This means that it is "easier" (or more probable) to have two people sharing the same birthday than not once the number of people concerned is over 21.
The probability would be different if you consider year as well as month and day, but most students of the same form would have been born in the same year (or within a year, say, Sept 1986 - Aug 1987), so this result should still hold, at least approximately.
If there are 40 students in each class, the probability that everyone has a different birthday from everyone else is 364/365 * 363/365 * 362/365 * ... *325/365 = 0.0968 so there is an over 90% chance that two of your classmates share the same brithday.
If there are 200 students in each form, the probability that everyone has a different birthday from everyone else is 364/365 * 363/365 * 362/365 * ... *165/365 = 7e-31 so I can almost say with certainty that two of your "form-mates" share the same birthday.
On the other hand, there is only a chance of 1-(364/365)^199 = 42% that someone in your form share your birthday and a chance of 1-(364/365)^39 = 10% that someone in your class share your birthday.

Good luck ... and have fun looking for your ... "birth-mates"!

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Replies:

Subject	Author	Date
Re: 和自己同年同月同日出生的人	祖	21:34:40 12/28/01 Fri
Re: 和自己同年同月同日出生的人 -- 人一個, 11:32:53 12/29/01 Sat