# Birthday match dating

*02-Jul-2017 16:19*

randomly chosen people, some pair of them will have the same birthday.By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29).A related question is, as people enter a room one at a time, which one is most likely to be the first to have the same birthday as someone already in the room?That is, for what ; a similar approximate pattern can be found using a number of possibilities different from 365, or a target probability different from 50%.This continues until finally the probability of Event 23 given that all preceding events occurred is 343/365.Finally, the principle of conditional probability implies that The white fields in this table show the number of hashes needed to achieve the given probability of collision (column) given a hash space of a certain size in bits (row).A formal proof that the probability of two matching birthdays is least for a uniform distribution of birthdays was given by Bloom (Bloom 1973).

Further results were that psychology students and women did better on the task than casino visitors/personnel or men, but were less confident about their estimates.Using the birthday analogy: the "hash space size" resembles the "available days", the "probability of collision" resembles the "probability of shared birthday", and the "required number of hashed elements" resembles the "required number of people in a group".One could of course also use this chart to determine the minimum hash size required (given upper bounds on the hashes and probability of error), or the probability of collision (for fixed number of hashes and probability of error).It may be shown people is needed; but on average, only 25 people are required.

An informal demonstration of the problem can be made from the list of Prime Ministers of Australia, of which there have been 29 as of 2017, in which Paul Keating, the 24th Prime Minister, and Edmund Barton, the first Prime Minister, share the same birthday, 18 January.Another generalization is to ask what is the probability of finding at least one pair in a group of people have at least one shared birthday], this average is determining the Mean of the distribution, as opposed to the customary formulation which determines the Median.