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:
“Since mothers are more likely to take children to their activities—the playground, ballet or karate class, birthday parties—they get a chance to see other children in action.... Fathers usually don’t spend as much time with other people’s kids; because of this, they have a narrower view of what constitutes “normal” behavior, and therefore what should or shouldn’t require parental discipline.”
—Ron Taffel (20th century)
“I used to be a discipline problem, which caused me embarrassment until I realized that being a discipline problem in a racist society is sometimes an honor.”
—Ishmael Reed (b. 1938)