Pascal and Probability: Volume 1 in the "Scientist and Science" series

ISBN-13: 9781492722618 / Angielski / Miękka / 2013 / 214 str.

Enders Anthony Robinson

Opis

This book can serve either as an interesting book to read for enjoyment or else as an introductory book on probability theory. It explains how probabilities are involved in daily life and in games off chance. The inauguration of the probability theory is primarily attributed to Blaise Pascal (1623-1662) and Pierre de Fermat (1601-1665). Passages from the writings of Pascal are scattered throughout the book. While contemplating a gambling problem posed by Chevalier de Mere in 1654, Blaise Pascal corresponded with Pierre de Fermat, and together they laid the fundamental groundwork of probability theory. One of Pascal's letters discusses the "Problem of Points." Two players each need a given number of points in order to win; if they separate without playing out the game, how should the stakes be divided between them? This book treats the Problem of Points, and goes on to discuss probability models, mathematical formulation, experiments, the notion of probability, and Pascal's arithmetic triangle. Pascal devised the mathematical concept of expectation (or expected value), which is of prime use in the application of probability theory. The expectation explains the features of advantageous, equitable, and disadvantageous games. Applications are made to games of chance and to life insurance. The concepts of events and favorable chances are described in terms of dice games and roulette. The addition rule and the multiplication rule for probabilities are presented. The multiplication rule is displayed graphically by means of tree diagrams. Permutations and combinations are explained. The notion of geometric probability is presented, and a discussion of Bertrand's paradox is given. An abundant collection of problems with solutions appear throughout the book.