What is the birthday paradox?

Here’s a fun puzzle: How big does a random group of people have to be to have a 50% chance that at least two of the people will share a birthday? The answer is 23, which surprises many people. How is it possible?

When pondering this question, known as the “birthday problem” or “birthday paradox” in statistics, many people intuitively guess 183, as it is half of all possible birthdays, as there are generally 365 days in a year. Unfortunately, intuition often gets along poorly with this type of statistical problem.

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