A pump station consists of 4 electric pumps. The system worksif A and B work AND

Question

A pump station consists of 4 electric pumps. The system worksif A and B work AND either of the pumps C or D work. Assumethat each pump operates independently. The probability ofeach component is: (A=.9 B=.9 C=.8 D=.8). What is the probabilities that the entire system works, whatabout A, B, D works but not C? I'm not sure where to apply the data to the formula. [P(C or D) is P(C) P(D) - P(C) P(D)] A pump station consists of 4 electric pumps. The system worksif A and B work AND either of the pumps C or D work. Assumethat each pump operates independently. The probability ofeach component is: (A=.9 B=.9 C=.8 D=.8). What is the probabilities that the entire system works, whatabout A, B, D works but not C? I'm not sure where to apply the data to the formula. [P(C or D) is P(C) P(D) - P(C) P(D)]

Explanation / Answer

We need to consider the following cases for the entire system towork: 1) A, B, C and D work: prob = 0.9(0.9)(0.8)(0.8) = 0.5184 2) Only A and B and C work: prob = 0.9(0.9)(0.8)(0.2) = 0.1296 3) Only A and B and D work: prob = 0.9(0.9)(0.2)(0.8) = 0.1296 4) Only A, C and D work prob = 0.9(0.1)(0.8)(0.8) = 0.0576 5) Only B, C and D work prob = 0.1(0.9)(0.8)(0.8) = 0.0576 Therefore, P(system works) = 0.5184+0.1296+0.1296+0.0576+0.0576 = 0.8928

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