Birthday problem: Difference between revisions

{{Wikipedia pre 15 June 2009|pagename=Birthday Problem|lang=en|oldid=296054030|timedate=21:44, 12 June 2009}}

 

In [[wp:probability theory|probability theory]], the '''birthday problem''', or '''birthday [[wp:paradox|paradox]]''' This is not a paradox in the sense of leading to a [[wp:logic|logic]]al contradiction, but is called a paradox because the mathematical truth contradicts naïve [[wp:intuition (knowledge)|intuition]]: most people estimate that the chance is much lower than 50%. pertains to the [[wp:probability|probability]] that in a set of [[wp:random|random]]ly chosen people some pair of them will have the same [[wp:birthday|birthday]]. In a group of at least 23 randomly chosen people, there is more than 50% probability that some pair of them will both have been born on the same day. For 57 or more people, the probability is more than 99%, and it reaches 100% when the number of people reaches 366 (by the [[wp:pigeon hole principle|pigeon hole principle]], ignoring leap years). The mathematics behind this problem leads to a well-known cryptographic attack called the [[wp:birthday attack|birthday attack]].

 

;Task

Using simulation, estimate the number of independent people required in a groups before we can expect a ''better than even chance'' that at least 2 independent people in a group share a common birthday. Furthermore: Simulate and thus estimate when we can expect a ''better than even chance'' that at least 3, 4 & 5 independent people of the group share a common birthday. For simplicity assume that all of the people are alive...

 

;Suggestions for improvement

* Kudos (κῦδος) for finding the solution by proof (in a programming language) rather than by construction and simulation.

 

;See also

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