Birthday Problem

In: Science

Submitted By fogelly
Words 2471
Pages 10
Birthday Problem

Subject: Mathematics
Name:Dmitry Kozyrev
Passport Number:N07797989
Date: 16.06.2015
Mark:

Contents
Abstract _______________________________________________ 3
Keywords______________________________________________ 3
1. Basis of Probability ___________________________________ 4
1.1 Conditional Probability _____________________________ 4
1.2 Independence _____________________________________ 4
2. Birthday Problem______________________________________5
2.1 What is Birthday Problem? _________________________ 5
2.2 Understanding the probability_________________________ 6
2.3 Calculating the probability of birthday problem___________ 7
2.4 Abstract proof______________________________________10
3 Examples______________________________________________11
4 References_____________________________________________13

2

Abstract
The subject of probability can be traced back to the 17th century when it arose out of the study of gambling games. As we see, the range of applications extends beyond games into business decisions, insurance, law, medical tests, and the social sciences. The stock market, “the largest casino in the world,” cannot do without it. The telephone network, call centers, and airline companies with their randomly fluctuating loads could not have been economically designed without probability theory. To quote Pierre-Simon, marquis de Laplace from several hundred years ago:
«It is remarkable that this science, which originated in the consideration of games of chance, should become the most important object of human knowledge...The most important questions of life are, for the most part, really only problems of probability.»

Keywords: experiment; outcomes; empty set; union; intersection; probability; birthday problem.

3

1. Basis of probability
1.1 Conditional Probability
Conditional Probability is…...

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...which will never let go.
 It is something that hurts a lot, just like the pain love can give us. And force us to feel and show. 
 People are forced to show their emotions. Confront them. Feel them. 
 This will somehow cause the trouble inside that human being the love is haunting, and in the worst scenarios even cause a pain that will just keep growing. 
 A pain, which will just get bigger the more the person notices it. 
 This is something we can see in the main character of the short story ‘’A Birthday Remembered.’’ 
 
 Ellen can be seen as a woman who has accepted the way she loves other people. She is a woman, who likes other women and that has caused her some problems in her life. 
 People live on the prejudices for lesbians and gay people in general, which can be the kind of main reason for some of her problems. 
 Ellen has found her one and true love, called Jackie. 
 
 Jackie left her husband so she could be with Ellen, which caused them some more problems now with the ex husband, Roger, nipping on their heels. 
 Which we can see in this quotation ‘’The three of them had survived through the tumultuous stress of trying to make it, ever since Jackie walked out on Roger and came to live with her.’’(I 10-11)
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