The Pleasures of Probability

1. Front Matter

   Pages i-xv

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2. Cars, Goats, and Sample Spaces

   • Richard Isaac

   Pages 1-11

3. How to Count: Birthdays and Lotteries

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   Pages 13-20

4. Conditional Probability: From Kings to Prisoners

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   Pages 21-30

5. The Formula of Thomas Bayes and Other Matters

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   Pages 31-40

6. The Idea of Independence, with Applications

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   Pages 41-53

7. A Little Bit About Games

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   Pages 55-59

8. Random Variables, Expectations, and More About Games

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   Pages 61-76

9. Baseball Cards, The Law of Large Numbers, and Bad News for Gamblers

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   Pages 77-93

10. From Traffic to Chocolate Chip Cookies with the Poisson Distribution

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    Pages 95-102

11. The Desperate Case of the Gambler’s Ruin

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    Pages 103-110

12. Breaking Sticks, Tossing Needles, and More: Probability on Continuous Sample Spaces

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    Pages 111-125

13. Normal Distributions, and Order from Diversity via the Central Limit Theorem

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    Pages 127-139

14. Random Numbers:What They Are and How to Use Them

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    Pages 141-155

15. Computers and Probability

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    Pages 157-168

16. Statistics: Applying Probability to Make Decisions

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    Pages 169-186

17. Roaming the Number Line With a Markov Chain: Dependence

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    Pages 187-202

18. The Brownian Motion, and Other Processes in Continuous Time

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    Pages 203-214

19. Back Matter

    Pages 215-244

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The ideas of probability are all around us. Lotteries, casino gambling, the al­ most non-stop polling which seems to mold public policy more and more­ these are a few of the areas where principles of probability impinge in a direct way on the lives and fortunes of the general public. At a more re­ moved level there is modern science which uses probability and its offshoots like statistics and the theory of random processes to build mathematical descriptions of the real world. In fact, twentieth-century physics, in embrac­ ing quantum mechanics, has a world view that is at its core probabilistic in nature, contrary to the deterministic one of classical physics. In addition to all this muscular evidence of the importance of probability ideas it should also be said that probability can be lots of fun. It is a subject where you can start thinking about amusing, interesting, and often difficult problems with very little mathematical background. In this book, I wanted to introduce a reader with at least a fairly decent mathematical background in elementary algebra to this world of probabil­ ity, to the way of thinking typical of probability, and the kinds of problems to which probability can be applied. I have used examples from a wide variety of fields to motivate the discussion of concepts.

• Brownian motion
• Law of large numbers
• Markov chain
• Poisson distribution
• Radiologieinformationssystem
• Random variable
• statistics

• Department of Mathematics, Lehman College, City University of New York, Bronx, USA

  Richard Isaac

• The Graduate Center, New York, USA

  Richard Isaac

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