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Birthday problem - Wikipedia

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In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share a birthday. The birthday paradox refers to the counterintuitive fact that only 23 people are needed for that probability to exceed 50%. The birthday paradox is a veridical paradox: it seems wrong at first glance but is, in fact, true. While it may seem surprising that only 23 individuals are required to reach a 50% probability of a shared birthday, this result is made more intuitive by considering that the birthday comparisons will be made between every possible pair of individuals. With 23 individuals, there are 23 × 22 / 2 = 253 pairs to consider, far more than half the number of days in a year. Real-world applications for the birthday problem include a cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of finding a collision for a hash function, as well as calculating the approximate risk

Birthday problem - Wikipedia Jump to content From Wikipedia, the free encyclopedia Probability of shared birthdays For yearly variation in mortality rates, see Birthday effect . For the mathematical brain teaser that was asked in the Math Olympiad, see Cheryl's Birthday . The computed probability of at least two people sharing the same birthday versus the number of people In probability theory , the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday . The birthday paradox is the counterintuitive fact that only 23 peop

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