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An inspector of the Alaska Pipeline has the task of comparing the reliability of two pumping stations. Each station is susceptible to two kinds of failure: pump failure and leakage. When either (or both) occurs, the station must be shut down. The data at hand indicate that the following probabilities prevail:StationP (Pump Failure)P (Leakage)P (Both)10.070.10020.090.120.06Which station has the higher probability of being shut down? |
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Answer» Let A = Event which indicates pump failure. B = Event which indicates pump is leakaged For station 1, P(A) = 0.07, P(B) = 0.1 P(A ∪ B) = 0 ∴ P(A ∪ B)1 = P(A) + P(B) - P(A ∪ B) = 0.07 + 0.1 - 0 = 0.17 For station 2, P(A) = 0.09, P(B) = 0.12 P(A ∪ B) = 0.06 ∴ P(A ∪ B)2 = P(A) + P(B) - P(A ∪ B) = 0.09 + 0.12 - 0.06 = 0.21 - 0.06 = 0.15 ∴ P(A ∪ B)1 > P(A ∪ B)2 Thus, station 1 has the higher probability of being shut down. |
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