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# sta4321-7 - Bayes Rule Theorem of Total Probability Bayes...

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Bayes’ Rule

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Theorem of Total Probability Bayes’ Rule Odds, Odds Ratios, and Relative Risk Partition Definition (Partition) Events B 1 , B 2 , . . . , B k are said to partition a sample space S if 1 they are mutually exclusive ( B i B j = for any pair i and j ) 2 k j = 1 B j = S Arthur Berg Bayes’ Rule 2/ 8
Theorem of Total Probability Bayes’ Rule Odds, Odds Ratios, and Relative Risk Partition Theorem (Theorem of Total Probability) If B 1 , B 2 , . . . , B k is a partition of the sample space, then for any event A, P ( A ) = k i = 1 P ( AB i ) = k i = 1 P ( B i ) P ( A | B i ) Arthur Berg Bayes’ Rule 3/ 8

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Theorem of Total Probability Bayes’ Rule Odds, Odds Ratios, and Relative Risk Partition Example Example (Exercise 3.43 slightly modified) John flies frequently and likes to upgrade his seat to first class. He has determined that, if he checks in for his flight at least two hours early, the probability that he will get the upgrade is .75; otherwise, the probability that he will get the upgrade is .35. With his busy schedule, he checks in at least two hours before his flight only 40% of the time. What is the probability that, for a randomly selected trip, John will be able to upgrade to first class?
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sta4321-7 - Bayes Rule Theorem of Total Probability Bayes...

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