Birthday Paradox

[Source]

• If 23 people are in a room together, there is about a 50% chance that two of them share a birthday.
• If 48 people are in a room together, there is about a 95% chance that two of them share a birthday.
• If 88 people are in a room together, there is about a 50% chance that three of them share a birthday.
• In a crowd of 1813 there is a 50% chance that thirteen of them share one birthday.

Why?

When you put 20 people in a room, however, the thing that changes is the fact that each of the 20 people is now asking each of the other 19 people about their birthdays. Each individual person only has a small (less than 5%) chance of success, but each person is trying it 19 times. That increases the probability dramatically. [1]