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Unformatted text preview: Introducing Probability: Chapter 5 Section 5.1 Probability Rules: A Introduction: Probability =Mathematics of Chance. Probability is a measure of the likelihood of a given event. B (a) Formal Definition: Probability= p = f/N = Number of successes / number of trials (b) f= number of successes in N-Trials of a random experiment. N= Number of Trials. p = probability of success, when an experiment is repeated many times. C Example What proportion of adults played the lottery last year? In a sample of 1523 adults we found that 868 answered yes to this question Hence p = 868/1523 = 57=57% adults we found that 868 answered yes to this question. Hence, p = 868/1523 = .57=57%. If we chose another sample, we might get the sample proportion of, say "p = .54" or "p=.60" which is different due to chance. If sample proportion is "p=.37'", we should question our sampling procedure because "p=.37 is too far from what we expected. D Law of Large Numbers : As N increases, sample proportion approaches "TRUE" Probability. E Idea of Probability: (Chance behavior unpredictable in the short run, but over time quite predictable.) Example Toss a coin 5000 times. Trial A: Pattern=THTT. Trial B: HHHHH. Note: The pattern is quite different over the short run; but after 5000 tosses you expect something CLOSE to 2500 heads and 2500....
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