🎂 Birthday Paradox Calculator
Discover the surprisingly high chance that two people in a group share the same birthday.
What the birthday paradox is
The birthday paradox describes how quickly the probability of a shared birthday rises as a group grows, even though it feels like it should take many more people. With just 23 people, there is over a 50% chance that two of them share a birthday, because you are comparing every possible pair, not just one person against everyone else.
How the calculation works
The calculator first finds the probability that everyone has a different birthday by multiplying the shrinking odds of each additional person avoiding all previously used birthdays. Subtracting that result from 1 gives the probability that at least one pair shares a birthday. You can adjust the number of possible birthdays if you want to model something other than a standard 365-day year.
This is a classic probability exercise used for education and general curiosity, based on the standard combinatorics formula for the birthday problem.