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13.1 Theoretical Probability

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The overall likelihood, or probability, of an event can be discovered by observing the results of a large number of repetitions of the situation in which the event may occur. Outcomes are random if all possible outcomes are equally likely. The sum of the probabilities is 1.

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Definition/Example : Trial: a systematic opportunity for an event to occur rolling a # cube Experiment: 1 or more trials rolling a # cube 10 times Sample Space: the set of all possible outcomes 1, 2, 3, 4, 5, 6 of an event Event: an individual outcome rolling a 3 or any specified combination of outcome rolling a 3 or rolling a 5

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1 st toss2 nd toss3 rd toss HHH HHT HTT THH TTH TTT HTH THT

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Theoretical Probability: is based on the assumption that all outcomes in the sample space occur randomly. If all outcomes in a sample space are equally likely, then the theoretical probability of event A, denoted P(A), is defined by: P(A) = ___number of outcomes in event A___ number of outcomes in the sample space

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2/9 = 22.2%

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4/9 = 44.4%

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2/15 = 13.3%

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a). from 1:30 p.m. to 1:40 p.m. 10/60 = 1/6 = 16.6% b). from 1:30 p.m. to 1:35 p.m. 5/60 = 1/12 = 8.3%

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a). 8:04 a.m. 1/5 = 20% b). 8:02 a.m. 3/5 = 60% c). 8:01 a.m. 4/5 = 80% d). 8:03 a.m. 2/5 = 40%

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