Lesson9S1.pptx - TAIBAH UNIVERSITY Faculty of...

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TAIBAH UNIVERSITY Faculty of Science Department of Math . ةبيط ةعماج مولعلا ةيلك تايضايرلا مسق Probability and Statistics for Engineers STAT 305 Teacher : Dr. Moustapha Abdellahi First Semester 1438/1439
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Conditional Probability Bayes’ Rule Lesson 9
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The probability of an event B occurring when it is known that some event A has occurred is called a conditional probability and is denoted by P(B|A) . The symbol P (B | A) is usually read " the probability that B occurs given that A occurs " or simply " the probability of B , given A. "
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Definition 1 : The conditional probability of B, given A, denoted by P(B|A) is defined by provided P(A) > 0 .
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Example : Suppose that our sample space S is the population of adults in a small town who have completed the requirements for a college degree. We shall categorize them according to gender and employment status. The data are given in the following table.
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One of these individuals is to be selected at random for a tour throughout the country to publicize the advantages of establishing new industries in the town. We shall be concerned with the following events: M : a man is chosen , E : the one chosen is employed . What is ?
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Solution : Let denote the number of elements in any set A , then we write where and are found from the original sample space S. To verify this result, note that Hence
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The probability that a regularly scheduled flight departs on time is ; the probability that it arrives on time is 2 ; and the probability that it departs and arrives on time is . Find the probability that a plane (a)arrives on time given that it departed on time, (b)departed on time given that it has arrived on time.
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(a)The probability that a plane arrives on time given that it departed on time is (b) The probability that a plane departed on time given that it has arrived on time is
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Independent Events :
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