Math IA Final
Angeline Foote 00215-‐0022
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
1
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
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
1
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>.