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AnalysisBasic Probability ConceptsProbability PropertiesEventsCalculating ProbabilitiesCalculating ProbabilitiesConditional ProbabilityTree DiagramCalculation of Joint ProbabilitiesIndependent EventsAnalysisAnalysis is the examination of processes, facts, and data to gain an understanding of why problems occur and where opportunities for improvement exist. –Statistical inference is the process of drawing conclusions about unknown characteristics of a population from which data were taken.–Predictive statistics focus on cause-and-effect relationships and predictions of future performance from historical data.1Basic Probability ConceptsAn experiment is a process that results in some outcome.The outcome of an experiment is a result that we observeThe collection of all possible outcomes of an experiment is called the sample space.Probability is the likelihood that an outcome occurs.2Probability PropertiesLabel the n outcomes in a sample space as O1, O2, … On, where Oi represents the ith outcome in the sample space.The probability associated with any outcome must be between 0 and 1–0 ≤ P(Oi) ≤ 1 for each outcome OiThe sum of the probabilities over all possible outcomes must be 1.0–P(O1) + P(O2) + … + P(On) = 13EventsAn event is a collection of one or more outcomes from a sample spaceIf A is any event, the complement of A, denoted as Ac, consists of all outcomes in the sample space not in A.Two events are mutually exclusive if they have no outcomes in common.4Calculating ProbabilitiesRule 1: The probability of any event is the sum of the probabilities of the outcomes that compose that event.Rule 2: The probability of the complement of any event A is P(Ac) = 1 – P(A).5Calculating ProbabilitiesRule 3: If events A and B are mutually exclusive, then P(A or B) = P(A) + P(B)Rule 4: If two events A and B are not mutually exclusive, then P(A or B) = P(A) + P(B) – P(A and B)6Conditional ProbabilityConditional probability is the probability of occurrence of one event A, given that another event B is known to be true or have already occurred.Multiplication rule of probability:7Tree Diagram8Calculation of Joint Probabilities 9Independent EventsTwo events A and B are independent if P(A | B) =

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