Possibility of Sharing Brithdays

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Introduction:
While growing up I went to six different schools, and met around 1,000 people. However the only person I have met with my birthday, May 13th, was my great grandmother, out of the cumulative 1,000 people that I’ve gone to school with, not one has had the same birthday as mine. This is why I chose to investigate the paradox. According to the paradox, I should have met someone who had the same birthday as mine. The aim of this exploration will be to see if the paradox proves true in any given situation.
The Paradox:
The birthday paradox states that in a room of 23 people there is a 50% chance that exactly two of those people share a birthday. In order to better understand the probability the plausible combinations of 23 people when two are chosen must be calculated, (23¦2). A combination is defined as a group where the order of each individual in the group does not matter. The plausible number of combinations is 253. The 253 possibilities is the sample space. The sample space is defined as the set of all possible outcomes of the experiment.
The general trend in calculating the probability is to find the probability that everyone has a unique birthday. To calculate it, the formula used will be the probability of independent events in a sample space of 23 people. Independent events are defined as two events in which the first event does not affect the outcome of the second event. The paradox involves independent events because the first person having a birthday in March, for example, does not affect the second person having a birthday in February, for example.

The formula: (365¦n) n!/〖365〗^n
As stated previously, the formula looks at the probability of everyone having a unique birthday. The first person...

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....uicu.edu. University of Illiniois at Urbana-Champagne, n.d. Web. 6 Nov. 2013. .
"Permutations, Combinations and Probability." Faculty.atu.edu. Arkansas Tech University, n.d. Web. 6 Nov. 2013. .
Roberts, Donna. "Complement of an Event." Complement of an Event. Regents Prep, 2012. Web. 06 Nov. 2013. .
Roberts, Donna. "Independent Events." Independent Events. Regents Prep, 2012. Web. 06 Nov. 2013. .
CELEBRATING THE BIRTHDAY PROBLEM
Author(s): NEVILLE SPENCER
Source: The Mathematics Teacher, Vol. 70, No. 4 (APRIL 1977), pp. 348-353
Publisher(s): National Council of Teachers of Mathematics
Stable URL: http://www.jstor.org/stable/27960843

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