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