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Example 2- /nat does the quantity, P(F nean? au âuiso

Example 2- /nat does the quantity, P(F nean? au âuiso

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Using the notation from Example 2-38, what does the quantity, P(F'|S) mean? EXAMPLE 2-38 Bayesian Network Bayesian networks are used on the Web sites of high-technology manufacturers to allow customers to quickly diagnose problems with products. An oversimplified example is presented here. A printer manufacturer obtained the following probabilities from a database of test results. Printer failures are associated with three types of problems: hardware, software, and other (such as connectors), with probabilities 0.1, 0.6, and 0.3, respectively. The probability of a printer falure given a hardware problem is 0.9, given a software problem is 0.2, and given any other type of problem is 0.5. If a customer enters the manufacturer's Web site to diagnose a printer failure, vwhat is the most likely cause of the problem? Let the events H, S, and O denote a hardware, softvare, or other problem, respectively, and let F denote a printer failure. The most likely cause of the problem is the one that corresponds to the largest of F(HIF), r(SIF), and P(OIF). In Bayes' Theorem the denominator is P(F) = P(FH)P(H) + P(FS)P(S) + P(F|O)P(O) =0.9(0.1) + 0.2(0.6) + 0.5(0.3) = 0.36 Then, P(HF) = P(FH)P(H)/ P(F) = 0.9(0.1) /0.36 0.250 P(SF) = P(F|S)P(S) I P(F) = 0.2(0.6) /0.36 = 0.333 P(OF) = P(F|0)P(O) I P(F) = 0.5(0.3) /0.36 = 0.417 Notice that P(HIF) + P(SIF) + P(OIF) = 1 because one of the three types of problems is responsible for the failure. Because P(OIF) is largest, the most likely cause of the problem is in the other category. A Web site dialog to diagnose the problem quickly should start with a check into that type of problem. Practical Interpretation: Such networks are more commonly used to diagnose problems in areas as diverse as electronic products and healthcare. The probability that software works if it has a printer problem. O The probability that a printer works and the software works. O The probability that a printer works if it has software problem. O The probability that there is a software problem if the printer is working.
Transcribed Image Text:Using the notation from Example 2-38, what does the quantity, P(F'|S) mean? EXAMPLE 2-38 Bayesian Network Bayesian networks are used on the Web sites of high-technology manufacturers to allow customers to quickly diagnose problems with products. An oversimplified example is presented here. A printer manufacturer obtained the following probabilities from a database of test results. Printer failures are associated with three types of problems: hardware, software, and other (such as connectors), with probabilities 0.1, 0.6, and 0.3, respectively. The probability of a printer falure given a hardware problem is 0.9, given a software problem is 0.2, and given any other type of problem is 0.5. If a customer enters the manufacturer's Web site to diagnose a printer failure, vwhat is the most likely cause of the problem? Let the events H, S, and O denote a hardware, softvare, or other problem, respectively, and let F denote a printer failure. The most likely cause of the problem is the one that corresponds to the largest of F(HIF), r(SIF), and P(OIF). In Bayes' Theorem the denominator is P(F) = P(FH)P(H) + P(FS)P(S) + P(F|O)P(O) =0.9(0.1) + 0.2(0.6) + 0.5(0.3) = 0.36 Then, P(HF) = P(FH)P(H)/ P(F) = 0.9(0.1) /0.36 0.250 P(SF) = P(F|S)P(S) I P(F) = 0.2(0.6) /0.36 = 0.333 P(OF) = P(F|0)P(O) I P(F) = 0.5(0.3) /0.36 = 0.417 Notice that P(HIF) + P(SIF) + P(OIF) = 1 because one of the three types of problems is responsible for the failure. Because P(OIF) is largest, the most likely cause of the problem is in the other category. A Web site dialog to diagnose the problem quickly should start with a check into that type of problem. Practical Interpretation: Such networks are more commonly used to diagnose problems in areas as diverse as electronic products and healthcare. The probability that software works if it has a printer problem. O The probability that a printer works and the software works. O The probability that a printer works if it has software problem. O The probability that there is a software problem if the printer is working.
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