 # Probability TUTORIAL.pdf - CHAPTER 1: PROBABILITY 1.1...

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1CHAPTER1: PROBABILITY1.1Probability- express the degree of uncertainty. The value ranges between 0 and 1.0 ------------------------------------- 1impossibilitycertaintySome terminology1.Experiment - is the process by which an observation is made.2.Outcomes - the results from the experiment3.Sample Space - the set which consisting of all possible outcomes, denoted byS .4.Event - is a subset of the outcomes setExamples:ExperimentOutcomesSampleSpaceEventToss a coinHead, TailS = {Head, Tail}A = getting a headA= {head}Roll a dieonce1, 2, 3, 4, 5, 6S = {1, 2, 3, 4, 5,6 }B = getting oddnumbersB = {1, 3, 5}Toss a cointwiceHH, HT, TH, TTS = { HH, HT, TH,TT}C = getting at leastone headC = {HH, HT, TH}Take a testPass, FailS = { Pass, Fail}D = fail the examsD = {fail}SelectastudentMale, FemaleS = {Male, Female}E = a female studentE = {female}ChioceofhandsetHTC,Samsung,iphoneS={HTC, Samsung,iphone}F = buying a HTCF = {HTC}
21.2Basic Concepts of ProbabilityLet A be any event defined over S1.0P(A)1where P(A) = probability of an event A.3.P(A') = 1 - P(A) where A' is the complement of A.P(A) + P(A’) = 14.The intersection of A and B, writtenAB, whose outcomes belong toboth A and B where5.Events A and B are said to bemutually exclusiveif they have nooutcomes in common.Eg:P(AB) = 0.P(AB)= 06.Theunion of A and B, written asAB, event whose outcomes belong toeither A or B or both.P(AB) = P(A) + P(B) - P(AB)If A andB are mutually exclusive, P(AB) = P(A) + P(B).7.A and B are independent events ifP(AB)=P(A) P(B)n(S)n(A)P(A)2.Seventsinitemsofno.Aeventinitemsofno.An(S)B)n(AB)P(ABAABB
31.3Probability ApproachWays to express the sample spacei.X & Y axisii.Tree Diagramiii.Venn Diagramiv.Contingency tablev.Own imaginationExamples:

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