Understanding Probability: Chance Rules in Everyday Life
Using elementary examples, the author describes how probability applies to our daily lives. The concepts of probability theory are motivated by interesting and insightful practical situations. Many examples deal with lotteries and casino games. The style of the book is informal but precise. Before deriving the corresponding formulas, the author suggests to use simulations to give the reader insights into such key concepts as the law of large numbers. The first part of the book describes fundamentals of probability theory, whereas the second part is an introduction to mathematical statistics. The examples presented by the author show that uncertainty often leads to quite different results than analogous deterministic rules. If random influences are neglected and the calculations are based on fixed parameters then the result may be far from the real outcome. This is illustrated in the section ”Pitfall for averages”: If a gentleman would like to place $100,000 in an investment fund with the average rate of return being 14% and he wants to withdraw from the account an amount at the end of each year over some 20 years, he gets a quite different result if he calculates with a fixed yearly return of 14% or if the rate of return is considered to be a random variable with expectation 14%.
From many interesting examples, I would like to mention the following one called ”A coincidence problem”: Two people, perfect strangers to each other, meet. Both of them live in the same city and each has 500 acquaintances there. Assuming that for each of the two people the acquaintances represent a random sample from the inhabitants of the city, what is the probability of the two people having at least one acquaintance in common? Would you guess that this probability is as large as 22%? To summarize, the book is an easy and interesting read and a source of many examples, problems, and exercises. The publication can be recommended as a supplementary text to introductory courses on probability theory and mathematical statistics.