chap3 - Chapter 3 Probability 3.1 BasicConceptsof...

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Probability Chapter 3
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§  3.1 Basic Concepts of  Probability
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3 probability experiment  is an action through which  specific results (counts, measurements or responses) are  obtained. Probability Experiments Example: Rolling a die and observing the  number that is rolled is a probability  experiment. The result of a single trial in a probability experiment is  the  outcome . The set of all possible outcomes for an experiment is the  sample   space . Example: The sample space when rolling a die has six outcomes.    {1, 2, 3, 4, 5, 6}
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4 An  event  consists of one or more outcomes and is a subset  of the sample space. Events Example: A die is rolled.  Event  A  is rolling an even number. simple event  is an event that consists of a single  outcome. Events are represented  by uppercase letters. Example: A die is rolled.  Event  A  is rolling an even number.   This is not a simple event because the outcomes of  event  are {2, 4, 6}.
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5 Classical   (or  theoretical probability  is used when each  outcome in a sample space is equally likely to occur.  The  classical probability for event  E  is given by Classical Probability Example: A die is rolled.   Find the probability of Event  A : rolling a 5.  Number of outcomes  in event ( )  . Total number of outcomes in sample space P E = There is one outcome in Event  A : {5} 1 0.167 6 P(A ) =   “Probability of  Event  A .”
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6 Empirical  (or  statistical probability  is based on  observations obtained from probability experiments.  The  empirical frequency of an event  E  is the relative frequency of  event  E . Empirical Probability Example: A travel agent determines that in every 50 reservations  she makes, 12 will be for a cruise. What is the probability that the next reservation she  makes will be for a cruise? Frequency of Event  ( )  Total frequency E P E = 12 0.24 50 = P( cruise) =   f n =
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As an experiment is repeated over and over, the empirical  probability of an event approaches the theoretical (actual)  probability of the event.   Law of Large Numbers Example: Sally flips a coin 20 times and gets 3 heads.  The  empirical probability is         This is not representative of  the theoretical probability which is       As the number of  times Sally tosses the coin increases, the law of large  numbers indicates that the empirical probability will get  closer and closer to the theoretical probability. 3
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This note was uploaded on 09/22/2011 for the course MATH 201 taught by Professor R during the Spring '11 term at Lee.

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chap3 - Chapter 3 Probability 3.1 BasicConceptsof...

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