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| ``Re: How many needed''
by CWoo on 2006-08-12 12:43:34 |
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| Suppose there are 365 days in a year and suppose you need x people to find two matching birthdays (not including year). The complement of this is that none of the x people have matching birthdays. There are 365 choices of birthdays for the first person picked, 364 choices remain for the 2nd person picked, etc... So the total number of choices for all x people having mutually distinct birthdays is
A(x) = 365*364*...*(365-x+1)
But there are
B(x) = 365^x
choices if we allow duplicate birthdays.
So the probability that at least two people have the same birthday is p(x) = 1 - A(x)/B(x). So we want to find the least positive integer x such that p(x)>= 0.5. Use a calculator or a spreadsheet application you find that x is 23. |
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