In a wedding party of 50 people, what is the probability that no 3 people share the same birthday?
Thank you for help.
1 - In such scenarios it is much easier to figure out the probability of 3 people out of 50 who share the same birthday.
2 - For that purpose, will use this nast-looking summation formula to figure out the probability of 3 of them sharing the same birthday: n=50; 1 - (a=sumfor(i,0,n/2,(1/2^i)*(365 nCr i)*((365 - i) nCr (n - 2*i))*(n!/365^n)).
3 - The above summation formula readily gives: 0.1263751842, or 12.64% probability of 3 people out of 50 sharing the same birthday.
4 - But, we want the opposite of not sharing the same birthday. So, all we have to do is to subtract the probability in (3) above from 1 and we have our answer.
5 - 1 - 0.1263751842 =0.8736248158 =~87.36% probability that no 3 people in that wedding party share the same birthday.