Birthday paradox

The birthday paradox states that if there are 23 people in a room then there is a chance of more than 50% that at least two of them will have the same birthday. This means that in a typically-sized school class, where the 'paradox' is often cited, an even higher probability often applies. For 60 or more people, the probability is already greater than 99%. This is not a paradox in the sense of leading to a logical contradiction; it is a paradox in the sense that it is a mathematical truth that contradicts common intuition. Most people estimate that the chance is much lower than 50:50. Calculating this probability (and related ones) is the birthday problem. The mathematics behind it has been used to devise a well-known cryptographic attack named the birthday attack.

References

• Zoe Emily Schnabel: "The estimation of the total fish population of a lake", American Mathematical Monthly 45 (1938), pages 348-352
• M. Klamkin and D. Newman: "Extensions of the birthday surprise", Journal of Combinatorial Theory 3 (1967), pages 279-282.