Lect7 - Conditional Probability Independence of Events Tree...

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Conditional Probability Independence of Events Tree Diagram Outline Conditional Probability Multiplication Rule Independence of Events “Independent” versus “Mutually Exclusive” Tree Diagram 1 / 18 ISOM 2500 Lect 7: Conditional Probability and Independence
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Conditional Probability Independence of Events Tree Diagram Multiplication Rule Amazon Case Revisited The following contingency table summarizes n = 17 , 619 visits to amazon.com during the fall season. Q1 : What’s the probability that the next visitor to Amazon from one of these hosts will make a purchase? Q2 : What’s the probability that the next visitor to Amazon from one of these hosts will be from MSN and make a purchase? Q3 : What’s the probability that the next visitor to Amazon from MSN will make a purchase? 2 / 18 ISOM 2500 Lect 7: Conditional Probability and Independence
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Conditional Probability Independence of Events Tree Diagram Multiplication Rule Amazon Case Revisited, ctd To answer these questions, we can use the long run relative frequency method – but what are the right relative frequencies to look at? Q1: (What’s the probability that the next visitor to Amazon from one of these hosts will make a purchase?) Q2: (What’s the probability that the next visitor to Amazon from one of these hosts will be from MSN and make a purchase?) Q3: (What’s the probability that the next visitor to Amazon from MSN will make a purchase?) 3 / 18 ISOM 2500 Lect 7: Conditional Probability and Independence
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Conditional Probability Independence of Events Tree Diagram Multiplication Rule Joint Probability and Marginal Probability Joint probabilities are displayed in cells of a contingency table, represent the probability of an intersection of two or more events. For Amazon example, there are six joint probabilities; e.g., P ( Yes and MSN ) = 1 . 62 % = 0 . 0162 Marginal probabilities are displayed in the margins of a contingency table. Each marginal probability is the probability of observing an outcome with a single attribute, regardless of its other attributes. For Amazon example, there are five marginal probabilities, e.g., P ( MSN ) = 41 . 19 % = 0 . 4119 (= 39 . 58 % + 1 . 62 %) A table with all the joint and marginal probabilities as above is called a probability table 4 / 18 ISOM 2500 Lect 7: Conditional Probability and Independence
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Lect7 - Conditional Probability Independence of Events Tree...

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