Engineers in charge of maintaining nuclear submarines must continually check for corrosion inside the pipes that are par

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Engineers in charge of maintaining nuclear submarines must
continually check for corrosion inside the pipes that are part of
the cooling systems. The condition inside the pipes cannot be
observed directly, but a non-destructive test can give an
indication of possible corrosion. However, this test is not
reliable. For a randomly chosen pipe, let E denote the event that
the pipe has internal corrosion, and let F denote the event that
the test merely indicates internal corrosion. The test has
probability p of detecting corrosion when it is present, but it
also has probability q of falsely indicating corrosion. Suppose at
the time of testing, one in every n pipe has corrosion. Suppose
p=0.9, q=0.08 and n=5 What is the probability that a pipe has no
corrosion, given that the test on the pipe indicates corrosion (3
dp)?