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In a world where we are constantly being asked to make decisions based on incomplete information, facility with basic probability is an essential skill. This book provides a solid foundation in basic probability theory designed for intellectually curious readers and those new to the subject. Through its conversational tone and careful pacing of mathematical development, the book balances a charming style with informative discussion. This text will immerse the reader in a mathematical view of the world, giving them a glimpse into what attracts mathematicians to the subject in the first place. Rather than simply writing out and memorizing formulas, the reader will come out with an understanding of what those formulas mean, and how and when to use them. Readers will also encounter settings where probabilistic reasoning does not apply or where intuition can be misleading. This book establishes simple principles of counting collections and sequences of alternatives, and elaborates on these techniques to solve real world problems both inside and outside the casino. Pair this book with the HarvardX online course for great videos and interactive learning: https://harvardx.link/fat-chance.
Highlights key definitions, formulas, and theorems in boxes for easy reference
Some twenty-five essential formulas are conveniently collected in the back of the book
More than 100 exercises and forty worked examples build up from simple problems to complex real-world problems
Part I. Counting:
1. Simple counting
2. The multiplication principle
3. The subtraction principle
4. Collections
5. Games of chance
Interlude
6. The binomial theorem
7. Advanced counting
Part II. Probability:
8. Expected value
9. Conditional probability
10. Unfair coins and loaded dice
11. Geometric probability
Part III. Probability in the Large:
12. Games and their payoffs
13. The normal distribution
14. Don't try this at home.
Description
In a world where we are constantly being asked to make decisions based on incomplete information, facility with basic probability is an essential skill. This book provides a solid foundation in basic probability theory designed for intellectually curious readers and those new to the subject. Through its conversational tone and careful pacing of mathematical development, the book balances a charming style with informative discussion. This text will immerse the reader in a mathematical view of the world, giving them a glimpse into what attracts mathematicians to the subject in the first place. Rather than simply writing out and memorizing formulas, the reader will come out with an understanding of what those formulas mean, and how and when to use them. Readers will also encounter settings where probabilistic reasoning does not apply or where intuition can be misleading. This book establishes simple principles of counting collections and sequences of alternatives, and elaborates on these techniques to solve real world problems both inside and outside the casino. Pair this book with the HarvardX online course for great videos and interactive learning: https://harvardx.link/fat-chance.
Highlights key definitions, formulas, and theorems in boxes for easy reference
Some twenty-five essential formulas are conveniently collected in the back of the book
More than 100 exercises and forty worked examples build up from simple problems to complex real-world problems
