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the birthday paradox essays
the birthday paradox essays
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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
The Monty Hall problem is a hallmark of modern statistics. It was first officially published in the “Ask Marilyn” column of Parade magazine, in which the world's highest IQ, Marilyn vos Savant, answered reader questions and solved an enormous variety of puzzles and riddles. The Monty Hall problem was sent in by a reader and published exactly as follows:
Among the men that were conscripted into the supposedly random draft, certain groups of men were found to have been more likely to be called into service. Using statistical analysis it was found that "A box plot of the data by months confirms the pattern: those born in the second half of the year tend to receive lower lottery numbers." (Starr 1) The pattern that Star is referring to shows that, when a line is drawn using the mean values of the lottery number that men received over the course of twelve months, the line decreased over the time span. When Starr says that men with later birthdays receive a lower lottery number, he is basically pointing out that those men are called into service before the men with earlier birthdays. Had this been a truly random lottery, the data should have shown an equal distribution of lower and higher numbers between all of the days of the year. Not only did the draft discriminate against certain groups, the legality of it has been challenged numerous times.
Saltus, Richard. "DNA Fingerprinting: Its A Chance Of Probabilties." The Boston Globe 22 August 1994: 25.
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William was born in 1564. We know this from the earliest record we have of his life; his baptism which happened on Wednesday, April the 26th, 1564. We don't actually know his birthday but from this record we assume he was born in 1564. Similarly by knowing the famous Bard's baptism date, we can guess that he was born three days earlier on St. George's day, though we have no conclusive proof of this.
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I chose this topic because when I first read the birthday problem in the textbook, I tried to solve it repeatedly but each time I would get a very low probability. After re reading the question for the 20th time I finally realized my error. I was considering the probability that people would have the same birthday as me when the question was focusing on the probability that anyone in the room has the same birthday. When I finally managed to solve the question I didn’t know what else this could be used for so I did more research. That is when I discovered that the birthday paradox can also be used to crack hashing algorithms and can be used in cryptography.
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