How does the birthday math trick work?

Answer 1

Are you referring to the problem that calculates the probability that two or more people have the same birthday? If so, it starts out with finding the probability that someone has a birthday. Assuming it is not a leap year this would be 365/365 or 100%. This also means that there is a 0% chance of someone else having the same birthday because, so far, there is only 1 person in the equation, and they cannot have 2 birthdays. When you add in a second person the equation becomes 365/365 (person1) X 364/365 (person2). This means a 00.3% chance of a matched birthday. The equation repeats in this way as you add more people with the odds increasing exponentially for each addition person added. At 23 people there is a 50.6% chance of the same birthday occurring between 2 of any of those 23 people. Once you reach around 40-50 people the odds are higher than 99% that two people share a birthday and then this number can only slightly increase by fractions of a percent, never quite reaching 100% but being so close, that mathmaticians consider it a 100% chance of occurring.