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4-1(cont)_trees

4-1(cont)_trees - Section 4.1(cont Probability Trees A...

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Section 4.1 (cont.) Probability Trees A Graphical Method for Complicated Probability Problems

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Example: Southwest Energy A Southwest Energy Company pipeline has 3 safety  shutoff valves in case the line starts to leak. The valves are designed to operate independently of  one another: 7% chance that valve 1 will fail 10% chance that valve 2 will fail 5% chance that valve 3 will fail  If there is a leak in the line, find the following  probabilities: a. That all three valves operate correctly b. That all three valves fail c. That only one valve operates correctly d. That at least one valve operates correctly
A: P(all three valves operate correctly) P(all three valves work) = .93*.90*.95 = .79515

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B: P(all three valves fail) P(all three valves fail) = .07*.10*.05 = .00035
C: P(only one valve operates correctly) P(only one valve operates correctly = P(only V1 works) +P(only V2 works) +P(only V3 works) = .93*.10*.05 +.07*.90*.05 +.07*.10*.95 = .01445

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