In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are 366 possible birthdays, including February 29). However, 99% probability is reached with just 57 people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (except February 29) is equally probable for a birthday.
The mathematics behind this problem led to a well-known cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of cracking a hash function.
Read more about Birthday Problem: Understanding The Problem, Calculating The Probability, Approximations, An Upper Bound, Partition Problem
Famous quotes containing the words birthday and/or problem:
“the birthday of my life
Is come, my love is come to me.”
—Christina Georgina Rossetti (1830–1894)
“It is very comforting to believe that leaders who do terrible things are, in fact, mad. That way, all we have to do is make sure we don’t put psychotics in high places and we’ve got the problem solved.”
—Tom Wolfe (b. 1931)