If a class has 23 students in it then the probability that at least two of the students share a birthday is about 0.5. Surprised? If there are 50 students in a class then it's virtually certain that two will share the same birthday. This seems to go against common sense but is absolutely correct. Let's look at the probabilities a step at a time.
For one person, there are 365 distinct birthdays. For two people, there are 364 different ways that the second could have a birthday without matching the first. If there is no match after two people, the third person has 363 different birthdays that do not match the other two. So, the probability of a match is 1 - (365)(364)(363)/(365)(365)(365). This leads to the following formula for calculating the probability of a match with N birthdays is 1 - (365)(364)(363)...(365 - N + 1)/(365)^N. Running this through a computer gives that a probability of over .5 is obtained after 23 dates! If you like please reshare as many times as possible!!