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The birthday paradox, also known as the birthday problem, is a counterintuitive result in probability theory. It states that in a group of 23 or more people, there is a 50% chance that at least two people will share the same birthday. This result is surprising because it seems that a much larger group would be needed to reach a 50% probability.

The paradox arises because the probability of any two people sharing a birthday is not 1/365 (the number of days in a year), but rather 1/365 for the first person, 2/365 for the second person (since they could share a birthday with the first person), 3/365 for the third person, and so on. This means that the probability of at least two people sharing a birthday increases rapidly as the group size increases.

The birthday paradox has applications in various fields, including computer science, cryptography, and information theory. It is also used in probability theory to illustrate the concept of the birthday problem and the importance of considering the probability of multiple events occurring simultaneously.