Lecture7 - lecture 7, Probability III 1/21 Contingency...

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Unformatted text preview: lecture 7, Probability III 1/21 Contingency Table & Probability Table Tree Diagram Bayes’ Rule lecture 7, Probability III Outline 1 Contingency Table & Probability Table 2 Tree Diagram 3 Bayes’ Rule lecture 7, Probability III 2/21 Contingency Table & Probability Table Tree Diagram Bayes’ Rule lecture 7, Probability III Contingency Table & Probability Table Example, Newspaper Subscribers • Known that in a city: • total number of households is 1,000,000 • number subscribing to Atlantic Journal is 650,000 • number subscribing to Beacon News is 500,000 • number subscribing to both is 250,000 What’s the probability that a randomly selected Beacon News subscriber also subscribes to Atlantic Journal? • A: = {the selected household subscribes to Atlantic Journal} • B: = {the selected household subscribes to Beacon News} • The probability we want to find for the above question is • Also interested in knowing What’s P ( A | ¯ B )? Are A and B independent? lecture 7, Probability III 3/21 Contingency Table & Probability Table Tree Diagram Bayes’ Rule lecture 7, Probability III Contingency Table & Probability Table Contingency Table We can use a contingency table to help us with the analysis: Subscribes to B Doesn’t subscribe to B Total Subscribes to A 250,000 ? 650,000 Doesn’t subscribe to A ? ? ? Total 500,000 ? 1,000,000 Subscribes to B Doesn’t subscribe to B Total Subscribes to A 250,000 400,000 650,000 Doesn’t subscribe to A 250,000 100,000 350,000 Total 500,000 500,000 1,000,000 lecture 7, Probability III 4/21 Contingency Table & Probability Table Tree Diagram Bayes’ Rule lecture 7, Probability III Contingency Table & Probability Table Example, Newspaper Subscribers, ctd Subscribes to B Doesn’t subscribe to B Total Subscribes to A 250,000 400,000 650,000 Doesn’t subscribe to A 250,000 100,000 350,000 Total 500,000 500,000 1,000,000 • Hence • P ( A ) = 650 , 000 1000 , 000 = . 65 • P ( B ) = 500 , 000 1000 , 000 = . 50 • P ( A ∩ B ) = 250 , 000 1000 , 000 = . 25 • P ( A ∩ ¯ B ) = 400 , 000 1000 , 000 = . 4 • ... lecture 7, Probability III 5/21 Contingency Table & Probability Table Tree Diagram Bayes’ Rule lecture 7, Probability III Contingency Table & Probability Table Example, Newspaper Subscribers, ctd What’s the probability that a randomly selected Beacon News subscriber also subscribes to Atlantic Journal?...
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Lecture7 - lecture 7, Probability III 1/21 Contingency...

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