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Home / Tips and Tricks / In your average school class, there's a 50% chance that two people share what?

In your average school class, there's a 50% chance that two people share what?



  Graph showing the calculations of the birthday paradox
Rajkiran g / Wikimedia

Answer: A birthday

In the field of probability theory, there is a problem known as birthday paradox, regarding the probability that in a selection of N randomly selected persons, some of whom have their birthday. This probability reaches 1

00 percent as soon as you reach a sample size of 367 people (to account for the 366 potential days, including February 29, +1).

It is fascinating, however, how quickly the probability of sharing a birthday increases. In a group of 23 people, about the size of a small class, the likelihood that two people have their birthday has already risen to 50 percent. To reach 99 percent, you only have to put together two classrooms. In a group of 57, there is a 99 percent chance of having a birthday together.

While this looks like a mathematical salon trick, the math behind the birthday paradox has actually been successfully used as a well-known cryptographic attack, the Birthday Attack, which uses probabilistic models to reduce the complexity of cracking hash functions.


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