Two pumps connected in parallel fail independently of one another on any given day. the probability that only the older pump will fail is .10, and the probability that only the newer pump will fail is .05. what is the probability that the pump- ing system will fail on any given day (which happens if both pumps fail)?

Answer : Probability that the pumping system will fail on any given day = 0.005

Explanation:

Probability that only older pump fail = P(A) = 0.10

Probability that only newer pump fail = P(B) = 0.05

Since they are independent events ,

then the conditions will be

P(A∩B) = P(A). P(B)

             = 0.10 ×0.05

             =  0.005

Hence, the probability will fail on any given day = 0.005

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