We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

In a large party of 100 people, what is the probability that at least 3 of them share the same birthday?

Thanks for any help.

Guest Nov 23, 2017

#1**+1 **

There is actually a rather complicated-looking summation formula that calculates the probability and looks like this: **1 - ∑365!100! / {n! (100-2n)! (365-100 +n )! 2^n 365^100}, n=0 to 50**

I summed up the first 25 terms and this is what I got:

0.0000003072 4892785157 735709

0.0000057176 0222881694 70586

0.0000508909 4268458230 219

0.0002886351 9731554141 541

0.0011725134 2701322632 6

0.0036356601 5220545585 22

0.0089549931 7932524642 57

0.0180040514 1305516981

0.0301304065 5435743848 6

0.0425931051 2915248603 5

0.0514369825 9415105677 2

0.0535378343 2065788517 8

0.0483676643 9980012911 8

0.0381427347 9231609518 2

0.0263757108 7405165721 6

0.0160515040 4620857996 3

0.0086219711 4581710867 67

0.0040969650 1255139206 62

0.0017251648 9044419630 59

0.0006445389 9539204962 057

0.0002138286 3864673084 781

0.0000630164 3196881678 332

0.0000164976 4999120274 6726

0.0000038355 0437597406 85323

0.0000007913 2162082163 957176

________________________________

**1 - 0.354135321464259511361245756459 =64.59% - This is the probability of at least 3 people sharing the same birthday !!!.**

Guest Nov 23, 2017

edited by
Guest
Nov 23, 2017

#3**+1 **

The time it took for you to type in all those numbers deserves a thumbs up :)

supermanaccz
Nov 24, 2017