Course Notes - Department of Mathematics and Statistics

Now using the complementary event rule we can substract thisprobability from 1, meaning there is a 50.73% chance that at least twoof the people share birthday so this seemingly remarkable coincidenceoccurs more often than not.The probability that someone in the room had the same birthday asFred is slightly different, since the probability of each of the otherpeople not sharing Fred’s birthday would be 364365, so the probability noone shares Fred’s birthday is (365 364)22= 0.9414. Using complimentaryevents this tells us the probability someone shares Fred’s Birthday is1 − 0.9414 = 0.0586. This is quite rare event, so would have beensurprising.An understanding of what we are actually asking, and a basic understandingof probability can make seemingly impossible conincidencesactually appear quite reasonable.59