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

Strategist
Chance and uncertainty

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%?