Content deleted Content added
m Reverted 1 edit by 41.89.226.3 (talk) to last revision by JayBeeEll |
No edit summary |
||
Line 6:
In [[probability theory]], the '''birthday problem''' asks for the probability that, in a set of {{mvar|n}} [[random]]ly chosen people, at least two will share a [[birthday]]. The '''birthday paradox''' is that, counterintuitively, the probability of a shared birthday exceeds 50% in a group of only 23 people.
The birthday paradox is a [[veridical paradox]]: it appears wrong, 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 comparisons of birthdays will be made between every possible pair of individuals. With 23 individuals, there are (23 × 22) / 2 = 253 pairs to consider, which is well over half the number of days in a year (182.5 or 183 or 365 C 2).
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 attack|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.
| |||