The theory of probability

  Introduction
  Foundation
  Calculating
  Presize definition
  Binomial distribution
  Hypergeometric distribution
  Combined events
  Inseparable events
  'Ion Saliu's Paradox'
  Combinatorics
  Markov Chains
  Random Walks
  Contacts

Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continued to in°uence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a wellestablished branch of mathematics that ¯nds applications in every area of scholarly activity from music to physics, and in daily experience from weather prediction to predicting the risks of new medical treatments.

Before the theory of probability was formed Gambling was popular. Gamblers were crafty enough to figure simple laws of probability by witnessing the events at first hand. The opportunity was limitless in then exploiting the often complex and sometimes seemingly contradictory laws of probability.

In the seventeenth century Galileo wrote down some ideas about dice games. This led to discussions and papers which formed the earlier parts of probability theory. There were and have been a variety of contributors to probability theory since then but it is still one of the least understood areas of mathematics.

We have written this paper to make my own contribution to the advance of probability by posting a public domain document on the Internet outlining basic probability laws. We hope to enrich a few people by publishing this and hopefully enable people to prove contradictions that often flow around concerning claims of laws of probability and associated events. Also We hope it will help people come to terms quickly with basic laws of probability and therefore avoid all the suffering We had to endure over many years!!

Most calculations are shown in spreadsheet style format (Mainly MS Excel) as people who read this are most likely to have access to the mentioned software. We welcome feedback and encourage readers to make suggestions. We am always adding or amending sections of this page so please re-visit on occasion.

One thing We have learnt about probability that should give many of you guidance is that sometimes the answer is easy, it's getting the right question which is the difficult bit.  We view a best introduction as necessarily the best treatise. Science goes into such details that sounds like a jargon and resembles a game. Kind of like a theory of word puzzles: Using a lot of jargon for little practical purposes. Theory of probability has undoubtedly its jargon. It also has that huge number of formulas and equations with no practical purpose but to torment sleepless students before exams.

We get our share of questions regarding various aspects of probability. We can also see in public forums plenty of probability problems. Who can answer all those questions? What We remark, however, is a deficiency in the introduction to theory of probability. Probably the essentials are skipped too fast in order to cover all those insomnia-causing topics.

We wrote previously a few pages dedicated to probability and odds. Since We am unable to respond to most private questions and requests, We try to put together now the essential introduction to theory of probability. We must start with the start: the mother of all probability formulas; the formula that gives birth to many other formulas. We must also formulate fundamental algorithms of analyzing a wide variety of probability problems. Then we must put on the table the most efficient instrument of answering (almost) all questions on probability.