Two pumps connect in parallel fail independently of one anot

Two pumps connect in parallel fail independently of one another on any given day. The probability that ONLY the older pump will fail is 0.10, and the probability that ONLY the newer pump will fail is 0.05. The pumping station fails when BOTH pumps fail.

What is the probability that the pumping station will fail on any given day?

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My thoughts:

Let\'s assume: O = Old pump fails, N = New pump fails

We are given P(O n ~N) = 0.10 and P(N n ~O) = 0.05.

The answer is NOT (0.10) * (0.05) = 0.005. That would only work if P(O) = 0.10 and P(N) = 0.05, but they\'re not.

If someone could help me that would be greatly appreciated.

Solution

independent\".

We are given that:
   P(old fails) = 0.10
   P(new fails) = 0.05

Since the events are independent:
   P(old AND new fail) = P(old fails)