Birthday Paradox — The Reason Why In a Group of 23 People, The Probability of a Shared Birthday Exceeds 50%
I think many of you feel that this probability is greater than your intuition. This is because you are mixing up the probability that there are two people with the same birthday with the probability that there is someone with the same birthday as you.
I will explain this paradox step by step, using concrete examples. This time, we will not consider leap years and assume that a year is 365 days long.
In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. In a group of 23 people, the probability of a shared birthday exceeds 50%, while a group of 70 has a 99.9% chance of a shared birthday.
quoted from Birthday problem - Wikipedia
We will use n to denote the number of people in the group we are considering. For example, n = 10 means there are 10 people.
In the following, we will discuss the three cases — (I) n = 3, (II) n = 10, and (III) the general case (when there are n people).
(I) n = 3
What is the probability that at least one pair of people (two people) out of three have the same birthday?
