File:Birthdaymatch.svg
Summary
In probability theory, the <a href="https://en.wikipedia.org/wiki/birthday_problem" class="extiw" title="w:birthday problem">birthday problem</a> 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 <a href="https://en.wikipedia.org/wiki/pigeonhole_principle" class="extiw" title="w:pigeonhole principle">pigeonhole principle</a>, 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.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 05:54, 6 January 2017 | | 720 × 540 (291 KB) | 127.0.0.1 (talk) | In probability theory, the <a href="https://en.wikipedia.org/wiki/birthday_problem" class="extiw" title="w:birthday problem">birthday problem</a> 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 <a href="https://en.wikipedia.org/wiki/pigeonhole_principle" class="extiw" title="w:pigeonhole principle">pigeonhole principle</a>, 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. |
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