Which station has the higher Probability to shut down?

Question

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: Station P (Pump Failure) P (Leakage) P (Both) 1 0.07 0.10 0 2 0.09 0.12 0.06 Which station has the higher probability of being shut down? Select the correct answer from above options

Answer 1

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.