In a group of 23 people, there is a 50% chance of two people having the same birthday. This probability increases as the group size increases, reaching 100% at 367 people. The birthday paradox is used in cryptography and is due to the box principle.
In any group of 23 people, the probability that two of them have the same birthday is 50 percent. This phenomenon, which holds in any group of randomly selected people, is called the birthday paradox. When 57 people are in the group, the probability is 99 percent, and the percentage increases only slightly as the group size increases, eventually reaching 100 percent at 367 people. If two people meet by chance, however, the probability that they have the same birthday is only 0.27 percent.
More facts about the birthday paradox:
The birthday paradox is actually used in mathematics to crack hashing algorithms and can be used in cryptography.
The reason the birthday paradox works is due to something called the box principle, which states that if there are n numbers of items inserted into m number of holes, and n is greater than m, then at least one hole will have two items in it.
The birthday paradox seems so surprising because people don’t tend to go around asking about the dates of other people’s birthdays. If they did, it would quickly become apparent that shared birthdays are relatively common.
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