Tuesday, April 22, 2008

What are the chances?



SM provides the idea for this post. Pardon us for the math...

In a group of people of size r, what is the probability that two people share the same birthday? (Discounting leap days...)

TC = Total potential combinations of unique birthdays = 365 * 364 * 363 * ... * 365-r+1.

Probability of all unique birthdays = TC / (365^^r).

Probability of not all unique birthdays = 1 - (TC/(365^^r)).

Some examples:



# peopleProb (all unique)Prob (not all unique)
------------------------------------------------
11.000 0
100.883 0.117
200.58850.4115
300.293 0.707
400.10870.8913

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