Chapter 4 Probability

Chapter 4 4.1 Probability and Sample Spaces 4.2 Probability and Events 4.3 Some Elementary Probability Rules 4.4 Conditional Probability and Independence 4.5 Bayes’ Theorem (Optional) 4.6 Counting Rules (Optional)

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Chapter 4ProbabilityCopyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinProbability4.1 Probability and Sample Spaces4.2 Probability and Events4.3 Some Elementary Probability Rules4.4 Conditional Probability and Independence4.5 Bayes’ Theorem (Optional)4.6 Counting Rules (Optional)4-*4.1 Probability and Sample SpacesAn experiment is any process of observation with an uncertain outcomeThe possible outcomes for an experiment are called the experimental outcomesProbability is a measure of the chance that an experimental outcome will occur when an experiment is carried outThe sample space of an experiment is the set of all possible experimental outcomesThe experimental outcomes in the sample space are called sample space outcomesLO4-1: Define a probability and a sample space.4-*Probability If E is an experimental outcome, then P(E) denotes the probability that E will occur and: Conditions0  P(E)  1 such that:If E can never occur, then P(E) = 0If E is certain to occur, then P(E) = 1The probabilities of all the experimental outcomes must sum to 1LO4-14-*Assigning Probabilities to Sample Space OutcomesClassical methodFor equally likely outcomesRelative frequency methodUsing the long run relative frequencySubjective methodAssessment based on experience, expertise or intuitionLO4-14-*4.2 Probability and EventsAn event is a set of sample space outcomesThe probability of an event is the sum of the probabilities of the sample space outcomesIf all outcomes equally likely, the probability of an event is just the ratio of the number of outcomes that correspond to the event divided by the total number of outcomesLO4-2: List the outcomesin a sample space and use the list to compute probabilities.4-*4.3 Some Elementary Probability RulesComplementUnionIntersectionAdditionConditional probabilityMultiplicationLO4-3: Use elementary profitability rules to compute probabilities.4-*4.4 Conditional Probability and IndependenceThe probability of an event A, given that the event B has occurred, is called the conditional probability of A given BDenoted as P(A|B) Further, P(A|B) = P(A∩B) / P(B)P(B) ≠ 0LO4-4: Compute conditional probabilities and assess independence.4-*4.5 Bayes’ TheoremS1, S2, , Sk represents k mutually exclusive possible states of nature, one of which must be trueP(S1), P(S2), , P(Sk) represents the prior probabilities of the k possible states of natureIf E is a particular outcome of an experiment designed to determine which is the true state of nature, then the posterior (or revised) probability of a state Si, given the experimental outcome E, is calculated using the formula on the next slideLO4-5: Use Bayes’ Theorem to update prior probabilities to posterior probabilities (Optional).4-*Bayes’ Theorem ContinuedLO4-54-*4.6 Counting Rules (Optional)A counting rule for multiple-step experiments (n1)(n2)(nk)A counting rule for combinations N!/n!(N-n)!LO4-6: Use elementarycounting rules to compute probabilities (Optional).4-*