Comments on: Understanding the Birthday Paradox http://betterexplained.com/articles/understanding-the-birthday-paradox/ Learning shouldn't hurt. Let's share the insights that made difficult ideas click. Fri, 20 Nov 2009 14:09:06 -0800 http://wordpress.org/?v=2.8.4 hourly 1 By: Roy http://betterexplained.com/articles/understanding-the-birthday-paradox/#comment-252549 Roy Sun, 13 Sep 2009 19:20:00 +0000 http://betterexplained.com/articles/understanding-the-birthday-paradox/#comment-252549 Aren't there 366 possible birthdays? (feb 29) Aren’t there 366 possible birthdays? (feb 29)

]]> By: Sean http://betterexplained.com/articles/understanding-the-birthday-paradox/#comment-252341 Sean Fri, 11 Sep 2009 20:06:34 +0000 http://betterexplained.com/articles/understanding-the-birthday-paradox/#comment-252341 The explanations given are all approximations, in order to get an exact result you follow the start to Appendix A, but don't attempt to simplify with e^x. The solution is actually fairly simple, for n possibilities (days in the year) and k events (people at the party) we get a probability of: 1 - (P(n-1,k-1)/(n^(k-1))). Where P(n,k) is the number of ways to pick k elements from a set of n, or n!/(n-k)!. This will give an exact solution, the probability of finding two people with the same birthday from a crowd of 23 is more accurately: 50.7297234% I hope that this makes sense, if it doesn't, look at the page on combinatorics and/or think about the fact that (1-(j/n)) = ((n-j)/n) with reference to Appendix A. The explanations given are all approximations, in order to get an exact result you follow the start to Appendix A, but don’t attempt to simplify with e^x. The solution is actually fairly simple, for n possibilities (days in the year) and k events (people at the party) we get a probability of:

1 – (P(n-1,k-1)/(n^(k-1))).
Where P(n,k) is the number of ways to pick k elements from a set of n, or n!/(n-k)!.

This will give an exact solution, the probability of finding two people with the same birthday from a crowd of 23 is more accurately: 50.7297234%

I hope that this makes sense, if it doesn’t, look at the page on combinatorics and/or think about the fact that (1-(j/n)) = ((n-j)/n) with reference to Appendix A.

]]> By: The Birthday Paradox | by Jeremia Froyland http://betterexplained.com/articles/understanding-the-birthday-paradox/#comment-249442 The Birthday Paradox | by Jeremia Froyland Sat, 01 Aug 2009 20:13:10 +0000 http://betterexplained.com/articles/understanding-the-birthday-paradox/#comment-249442 [...] The math gets somewhat complicated, but you can check it out in more detail: Understanding the Birthday Paradox and Wikipedia’s page. [...] [...] The math gets somewhat complicated, but you can check it out in more detail: Understanding the Birthday Paradox and Wikipedia’s page. [...]

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