656 Why This Is Important Anytime we are interested in measuring the chance that something happens, we can discuss probability. Probability is commonly associated with buying a lottery ticket, playing poker, spinning the roulette wheel, or some other form of gambling. Indeed, the branch of mathematics we call probability traces its beginnings to games of chance in the sixteenth and seventeenth centuries. While probability is still used to assess gaming outcomes, probability is also vital to many other branches of mathematics and to many fields of science. Probability theory is the foundation for the study of statistics, which we will discuss in Chapter 12, and probability plays a key role in the modern study of chemistry, physics, genetics, computer science, artificial intelligence, and quantum mechanics. Probability is also the basis for actuarial science, which is used throughout the insurance and financial industries, and probability is involved in minimizing risk to businesses when faced with difficult decisions. Anytime analysis involves making a difficult choice, probability can be used to help make the best choice. Throughout this chapter, we will introduce many basic aspects of probability that can help us make informed decisions in our daily lives. Sections 11. 1 Empirical and Theoretical Probabilities 11. 2 Odds 11. 3 Expected Value (Expectation) 11. 4 Tree Diagrams 11. 5 Or and And Problems 11. 6 Conditional Probability 11. 7 The Fundamental Counting Principle and Permutations 11. 8 Combinations 11. 9 Solving Probability Problems by Using Combinations 11. 10 Binomial Probability Formula b In addition to being used to assess gaming outcomes, probability is also vital to many areas of mathematics, science, and to many real life applications. Probability 11 ESB Professional/Shutterstock
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