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.
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 of a hash collision existing within the hashes of a given size of population.
The problem is generally attributed to Harold Davenport in about 1927, though he did not publish it at the time. Davenport did not claim to be its discoverer "because he could not believe that it had not been stated earlier".[1][2] The first publication of a version of the birthday problem was by Richard von Mises in 1939.[3]
^David Singmaster, Sources in Recreational Mathematics: An Annotated Bibliography, Eighth Preliminary Edition, 2004, section 8.B
^H.S.M. Coxeter, "Mathematical Recreations and Essays, 11th edition", 1940, p 45, as reported in I. J. Good, Probability and the weighing of evidence, 1950, p. 38
^Richard Von Mises, "Über Aufteilungs- und Besetzungswahrscheinlichkeiten", Revue de la faculté des sciences de l'Université d'Istanbul4:145-163, 1939, reprinted in Frank, P.; Goldstein, S.; Kac, M.; Prager, W.; Szegö, G.; Birkhoff, G., eds. (1964). Selected Papers of Richard von Mises. Vol. 2. Providence, Rhode Island: Amer. Math. Soc. pp. 313–334.
theory, the birthdayproblem asks for the probability that, in a set of n randomly chosen people, at least two will share a birthday. The birthday paradox...
A birthday attack is a bruteforce collision attack that exploits the mathematics behind the birthdayproblem in probability theory. This attack can be...
December 31, see List of days of the year List of birthday songs BirthdayproblemBirthday attack Half-birthday Death anniversary/Yahrzeit Unbirthday Sashtiabdhapoorthi...
birthdayproblem asks, for a set of n randomly chosen people, what is the probability that some pair of them will have the same birthday? The problem...
room for whom the probability of completely unique birthdays is less than 50% (the birthdayproblem, where for 1 person the probability is 365/365 (or...
"Happy Birthday to You", or simply "Happy Birthday", is a song traditionally sung to celebrate a person's birthday. According to the 1998 Guinness World...
This probability can be computed precisely based on analysis of the birthdayproblem. For example, the number of random version-4 UUIDs which need to be...
probability. An example is the birthdayproblem, which shows that the probability of two persons having the same birthday already exceeds 50% in a group...
the IV is chosen at random, the probability of collisions due to the birthdayproblem must be taken into account. Traditional stream ciphers such as RC4...
objects produced (where the serial number can be in any base); see birthdayproblem. For this, a cryptographically secure pseudorandom number generator...
assignment of k balls into n urns, related to the coupon collector's problem and birthdayproblem. Pólya urn: each time a ball of a particular colour is drawn...
Security Symposium. The algorithm is based on a generalization of the Birthdayproblem which finds colliding hash values. It has severe time-space trade-offs...
is virtually inevitable, even if n is much larger than m – see the birthdayproblem. In special cases when the keys are known in advance and the key set...
complexity of a problem due to how the combinatorics of the problem is affected by the input, constraints, and bounds of the problem. Combinatorial explosion...
a spirited manner." In probability theory, he proposed the famous "birthdayproblem". He also defined the impossibility of a gambling system. In solid...
function is inherently vulnerable to collisions using a birthday attack. Due to the birthdayproblem, these attacks are much faster than a brute force would...
{\displaystyle 10!=6!\cdot 7!=3!\cdot 5!\cdot 7!} . In a discussion of the birthdayproblem, the number λ = 1 365 ( 23 2 ) = 253 365 {\displaystyle \lambda ={\frac...
Coupon collector's problemBirthday paradox Birthdayproblem Index of coincidence Bible code Spurious relationship Monty Hall problem Probable prime Probabilistic...
novella influenced by Virginia Woolf's The Waves. Her third novel, The BirthdayProblem, is a post-apocalyptic science fiction story about a communicable mental...
Secular Problem of Evil". In Bar-Am, Nimrod; Gattei, Stefano (eds.). Encouraging Openness: Essays for Joseph Agassi on the Occasion of His 90th Birthday. Springer...
Daniel Dinu Equihash: Asymmetric Proof-of-Work Based on the Generalized BirthdayProblem, NDSS 2016, with Alex Biryukov Tradeoff Cryptanalysis of Memory-Hard...
The 3rd Birthday (Japanese: ザ・サード バースデイ, Hepburn: Za Sādo Bāsudei) is a role-playing shooter developed by HexaDrive and published by Square Enix for the...
later proved by Borgs, Chayes, and Pittel. A related problem, somewhat similar to the Birthday paradox, is that of determining the size of the input...