CHAPTER 11 Summary 753 Important Facts and Concepts Examples and Discussion Section 11.1 Empirical Probability P E E ( ) number of times event has occurred total number of times the experiment has been performed = ⎛ ⎝⎜ ⎞ ⎠⎟ The Law of Large Numbers Probability statements apply in practice to a large number of trials, not to a single trial. It is the relative frequency over the long run that is accurately predictable, not individual events or precise totals. Theoretical Probability P E E ( ) number of outcomes favorable to total number of possible outcomes = Probability Facts The probability of an event that cannot occur is 0. The probability of an event that must occur is 1. Every probability must be a number between 0 and 1 inclusively; that is, P E 0 ( ) 1 ≤ ≤ The sum of the probabilities of all possible outcomes of an event is 1. P A P A ( ) (not ) 1 + = Examples 1–2, page 659 Discussion, pages 658– 660 Examples 3–5, pages 663– 666 Discussion, page 663 Example 5, pages 665– 666 Section 11.2 Odds Against an Event P P P P E E E Odds against (event fails to occur) (event occurs) (failure) (success) Odds against event number of outcomes unfavorable to number of outcomes favorable to = = = Odds in Favor of an Event P P P P E E E Odds in favor (event occurs) (event fails to occur) (success) (failure) Odds in favor of event number of outcomes favorable to number of outcomes unfavorable to = = = Determining Probabilities from Odds The denominators of the probabilities are determined by adding the numbers in the odds statement. The numerators of the probabilities are the numbers given in the odds statements. Examples 1–3, pages 672 – 674 Example 3, page 674 Example 4, page 675 Section 11.3 Expected Value E PA P A P A P An n 1 1 2 2 3 3 = + + + + Fair Price Fair price expected value cost to play = + Examples 1–7, pages 680– 684 Examples 8–9, pages 685– 686 Summary CHAPTER 11
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