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**13.1 Theoretical Probability**

Objectives: List or describe the sample space of an experiment. Find the theoretical probability of a favorable outcome. Standard Addressed: D: Use theoretical probability distributions to make judgments about the likelihood of various outcomes in uncertain situations.

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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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**Terminology: 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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Ex. 1a.

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**Ex. 1b. Find the sample space for the experiment of tossing a coin 3 times.**

1st toss 2nd toss 3rd toss H T

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Ex. 2

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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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Ex. 3

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Ex. 4

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Ex. 5a. Find the probability of randomly selecting a red disk in one draw from a container that contains 2 red disks, 4 blue disks, and 3 yellow disks. 2/9 = 22.2%

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Ex. 5b. Find the probability of randomly selecting a blue disk in one draw from a container that contains 2 red disks, 4 blue disks, and 3 yellow disks. 4/9 = 44.4%

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Ex. 6 Find the probability of randomly selecting an orange marble in one draw from a jar containing 8 blue marbles, 5 red marbles, and 2 orange marbles. 2/15 = 13.3%

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Ex. 7 Blade logs his electronic mail once during the time interval from 1 to 2 p.m. Assuming that all times are equally likely, find the probability that he will log on during each time interval. 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.**

Ex. 8 A bus arrives at Jason’s house anytime from 8 to 8:05 a.m. If all times are equally likely, find the probability that Jason will catch the bus if he begins waiting at the given time. 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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