Birthday problem

Rare card · No. 21010

In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday. The birthday paradox is 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 (the number being less than 1/15th of the number of days in a year), 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 {\displaystyle {\frac {23\times 22}{2}}=253} pairs to consider. Real-world applications for...

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