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Unit 7 - Probability 7.2 Definition of Probability.

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1 Unit 7 - Probability 7.2 Definition of Probability

2 Simple Events Let S be a finite sample space with n outcomes; S = {s 1, s 2, s 3, …, s n }. The simple events are those that consist of exactly one point of the experiment: {s 1 }, {s 2 }, {s 3 }, …, {s n }.

3 Ex: An opinion poll is conducted among a group of registered voters. Their political party (D, R, I) and gender (m, f) are recorded. List the simple events of this experiment. {Dm}, {Df}, {Rm}, {Rf}, {Im}, {If} The simple events of an experiment are mutually exclusive; meaning, only one can occur.

4 Coin-Tossing Experiment In pairs, flip a coin 10 times and record the number of heads. Number tosses (n) Number heads (m) Relative Frequency of Heads (m/n)

5 Probability The probability of an event occurring is a measure of the proportion of the time that the event will occur in the long run. Suppose that in n trials an event E occurs m times. The relative frequency of the event E is m/n. If the relative frequency approaches some value P(E) as n becomes larger, then P(E) is called the empirical probability of E.

6 A probability distribution is a table that lists the probability of each simple event of an experiment. Ex. The table below represents the frequency of certain types of license plates observed by a family on a recent trip. Find the probability distribution. StateNumber Wisconsin45 Illinois80 Iowa20 Indiana5 Probability 45/150 = 0.300 80/150 = 0.533 20/150 = 0.133 5/150 = 0.033 Notice 150 total observations

7 Properties of Probability Distributions 1.The probability of each simple event is between 0 and 1 inclusive. 2.The sum of the probabilities of all events in a sample space is 1. Ex:.3 +.533 +.133 +.033 = 1 3.The probability of the union of two mutually exclusive events is given by the sum of their probabilities. Ex: P(Wisc)  P(Iowa) =.3 +.133 =.433

8 Homework: 7.2 Exercises #2, 4, 7, 10, 14, 18, 20, 24, 32, 40, 42

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