The birthday paradox

In probability theory, the birthday paradox states that given a group of 23 (or more) randomly chosen people, the probability is more than 50% that at least two of them will have the same birthday. For 60 or more people, the probability is greater than 99%, although it cannot actually be 100% unless there are at least 366 people. This is not a paradox in the sense of leading to a logical contradiction; it is described as a paradox because mathematical truth contradicts naïve intuition. 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.