What is the probability that two or more people in a party of 20 people will have the same birthday

Question

This is a question from grade 12 data management homework. We are learning about using permutations 

Answer 1

The 20th person is used as the starting birthday

 

The 19th person has 1/365 change of matching that

 

the 18th person has 2/365 chance of matching the first two

 

the 17th person has 3/365 chance of matching those three

 

etc etc etc.

 

So the sum of the first 19  integers is 19*20/2 = 190

 

190/365 = 38/73 = 52%

 

 

BTW the probability exceeds 92% for 25 or more