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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