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 percent once you reach a sample size of 367 people (to account for the 366 potential days, including Feb. 29th, +1).
What’s fascinating, however, is how quickly the probability of sharing a birthday climbs. In a group of 23 people, around the size of a small class, the chances of two people sharing a birthday have already climbed to 50 percent. To get to 99 percent, you’d just need to gather two classrooms together. In a group of 57 people, there is a 99 percent chance that there is a common birthday.
While this might seem like something of a mathematical parlor 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.
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