# Same birthday probability Calculator

## Calculates the probability that one or more pairs in a group have the same birthday.

 n persons in a group 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit Probability with same birthdays p(n) %
 (1) the probability that all birthdays of n persons are different.$\normal \\\vspace{5}\hspace{20}\overline{p}(n)={\large\frac{364}{365}}\times{\large\frac{363}{365}}\times{\large\frac{362}{365}}\times\cdots\\\hspace{50}={\large\frac{365\times364\times363\times\cdots\times(365-n+1)}{365^n}}\\\hspace{50}={\large\frac{365!}{365^n(365-n)!}}\\$(2) the probability that one or more pairs have the same birthday.$\normal\\\vspace{5}\hspace{20}p(n)=1-\overline{p}(n)\\$This calculation ignores the existence of leap years.

Same birthday probability
 [1-2] /2 Disp-Num5103050100200
[1]  2017/12/05 06:36   Female / 40 years old level / Others / A little /
Purpose of use
Settling an argument.
Comment/Request
In a random sample of "n" people, 2 are found to share the same birthday.
In a second random sample of people, 2 are found to share the same birthday.
What are the odds that both pairs of people share the same birthday?
[2]  2009/07/30 02:00   Male / More than 60 / Others / Very /
Purpose of use
Very useful for backing up a bet taken in a pub. Thank you - I won.
Comment/Request
I love this kind of "dispute" settler - in addition, the formulae are beautifully complex in appearance, so my non-maths friends are entirely bamboozled.

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