Mathematics SL

Inter’l School of Tanganyika 2014

The Birthday Paradox: An Exploration of Probability

Angeline Foote Candidate number: 00215-‐0022 Mathematics Standard Level Teacher: Mr. Michael Smith International School of Tanganyika 2014

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Angeline Foote 00215-‐0022

Mathematics SL

Inter’l School of Tanganyika 2014

Introduction The birthday paradox states that in a room of 23 people, there is a 0.5 probability that at least two people share the same birthday (Weisstein). At first glance, this statement sounds absurd, with most people claiming that there is a far smaller probability of this happening. However, mathematics reveals that this is untrue. The paradox is strange and counter-‐intuitive, yet completely correct.

The issue lies in the fact that large exponents are not intuitive. With small-‐scale probability problems, we are usually able to make the correct conclusions, however, when numbers go beyond our standard mental capabilities, exponents become misleading (Kalid). A good example is the probability of obtaining a “heads” after throwing up a fair coin. When done once, people would say that the probability is 0.5. Repeating the trial would mean that there is another 0.5 possibility of obtaining

Cited: 2013. Web. 2 Nov. 2013. Kalid. "Understanding the Birthday Paradox." BetterExplained. N.p., 26 Apr. 2007. Web. 29 Sept. 2013. <http://betterexplained.com/articles/understanding-the-birthdayparadox/>. May 2012. Web. 19 Jan. 2014. Nov. 2013. <http://cosmos.ucdavis.edu/archives/2011/cluster6/Sun_Jared.pdf>. Dec. 2006. Web. 1 Dec. 2013.<http://www.nytimes.com/2006/12/19/business/20 leonhardt-table.html?_r=0>.