In a group of 5000 people, what is the probability that there would be one day of the year upon which nobody's birthday falls?

Question

it doesn't need to be a particular day, just looking for probability of there existing any one day on which none of the 5000 people in the group have a birthday

Answer 1

Let's say that some one day out of 365 (no leap year complications, please!) is to be excluded. Then P(not born on that excluded day) = 364/365 for each person.

 

If we apply this 5,000 times, then the Probability that none of the 5,000 persons had this same Month & Day number as his birthday anniversary is (364/365)⁵⁰⁰⁰.