In a room filled with different dates, a single match is enough. The question is how many people are needed before a match becomes more likely than no match at all.
The Shared Birthday
Riddle statement
There are \(n\) people in a room.
Assume that:
- each birthday is equally likely to fall on any of the 365 days of the year;
- different people's birthdays are independent;
- leap years are ignored.
What is the smallest value of \(n\) for which the probability that at least two people share a birthday is greater than 50%?