In Your Average School Class There Is A 50% Chance Two People Share What?
Answer: A Birthday
In the field of probability theory, there is a problem known as the Birthday Paradox concerning the probability that in a selection of N randomly chosen people, some of them will share a birthday. This probability reaches 100% once you reach a sample size of 367 (to account for the 366 potential days, including Feb. 29, +1).
What’s fascinating, however is how quickly the probability of climbs. In a group of 23 people, around the size of your average primary or secondary classroom, the chances of two people sharing a birthday has already climbed to 50%. To get to 99%, you’d just need to gather two classrooms together. In a group of 57 people there is a 99% chance there is a common birthday. The change between 57 and 367 people is a hundredth of a percent per person added to the pool.
While this might seem like something of a mathematical parlour trick, the math behind the Birthday Paradox has actually been successfully employed as a well known cryptographic attack, the Birthday Attack, which uses probabilistic modeling to reduce the complexity of cracking encryption hash functions.