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probability 531 The theory of probabilities is simply the Science of logicquantitatively treated. PEIRCE IntroductionIn earlier Classes, we have studied the probability as ameasure of uncertainty of events in a random discussed the axiomatic approach formulated byRussian Mathematician, Kolmogorov (1903-1987)and treated probability as a function of outcomes of theexperiment. We have also established equivalence betweenthe axiomatic theory and the classical theory of probabilityin case of equally likely outcomes. On the basis of thisrelationship, we obtained probabilities of events associatedwith discrete sample spaces. We have also studied theaddition rule of probability . In this Chapter , we shall discussthe important concept of conditional probability of an eventgiven that another event has occurred, which will be helpfulin understanding the Bayes' theorem, multiplication rule ofprobability and independence of events.
PROBABILITY 533 Thus, we can also write the conditional probability of E given that F has occurred as P(E|F) = Numberof elementaryeventsfavourableto E F
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