Birthday Paradox

Post Reply
User avatar
Royal
Posts: 10562
Joined: Mon Apr 11, 2011 5:55 pm

Birthday Paradox

Post by Royal » Sun Dec 09, 2012 11:16 am

Martin Gardner writes, "Since the beginning of history, unusual coincidence have strengthened belief in the influence in life of occult forces. Events that seem to miraculously violate the laws of probability were attributed to the will of gods and devils, God or Satan, or at the very least to mysterious laws unknown to science and mathematics." One problem that has intrigued coincidence researchers is the birthday paradox.

Imagine you are in a large living room that people gradually enter. How many people must enter the room before the probability tat some share a birthday becomes at least 50 percent? This problem, posed in 1939 by Austrian-born American mathematician Richard von Mises, is significant because its solution is counterintuitive to most people, because it is one of the most explored probability problems in classrooms today, and because variations of the birthday problem serve as useful models for analyzing amazing coincidences in everyday life.

Assuming 365 days each year, the answer to the problem is a mere 23 people. In other words, if a room is filled with 23 or more randomly chosen people, there is more than a 50 percent probability that some pair of people will have the same birthday. For 57 or more people, the probability is more than 99 percent.

Just 23 people may have been fewer than you expected because we were not seeking two particular people or a specific birthday date. A match on any date for any two people is sufficient. In fact, 253 different pairings are possible among 23 people, any of which could lead to a match.


User avatar
Royal
Posts: 10562
Joined: Mon Apr 11, 2011 5:55 pm

Re: Birthday Paradox

Post by Royal » Wed Oct 03, 2018 9:23 am


Post Reply