In probability theory, the birthday problem concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 366 (since there are 365 possible birthdays, excluding February 29th). It would seem that we would need 183 people (half of 365) to reach a 50% probability. However, 99% probability is reached with just 57 people and 50% probability with just 23 people. These conclusions are based on the assumption that each day of the year (except February 29) is equally probable for a birthday.
Given a group of 20 people and performing 10,000 simulation runs, your program should report that 41.24% of the time there were two people that shared the same birthday. You can also see the image below:
