2.09 - The last example was an example of this method:...

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1 1 Chapter 2, Section 9 Calculating Probabilities © John J Currano, 01/27/2010 Event (De)Composition Method 2 The last example was an example of this method: 1. Decompose the event of interest into subevents whose probabilities (unconditional or conditional, as appropriate) are either known or easy to calculate. 2. Use the Rules of Probability and the Counting Tools to calculate the probability of the desired event. 3 Example . (p. 68, #2.113) There is a probability of 0.02 that a radar set will fail to detect a plane in its area. Find the probability that it will correctly detect exactly three aircraft before it fails to detect one, if aircraft arrivals are independent events occurring at different times. d d d f #1 #2 #3 #4 Let D k = event the set detects plane # k so D k = event the set fails to detect plane # k. We are given P ( D k ) = 0.02. Thus, P ( D k ) = 0.98. We want P ( D 1 D 2 D 3 D 4 ) = P ( D 1 ) P ( D 2 | D 1 ) P ( D 3 | D 1 D 2 ) P ( D 4 | D 1 D 2 D 3 ) = P ( D 1 ) P ( D 2 ) P ( D 3 ) P ( D 4 ) since arrivals independent = (0.98) 3 (0.02) = 0.0188 4 66 N 6 N N 666 6 N 6 N 6 2
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2.09 - The last example was an example of this method:...

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