Answer Happy

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 Fdenote 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 of falsely indicating corrosion. Suppose at the time of testing, one in every n pipe has corrosion. Suppose p=0.6.q=0.1 and 5 a) What is probability that a pipe has corrosion and the test detects corrosion (3 dp)?: (1 mark) b) What is the probability that a pipe has no corrosion, given that the test on the pipe indicates corrosion (3 dp)?: (1 mark) c) Suppose 10 pipes with internal corrossion are tested for corrosion. Assume that the test result for pipes are independent of each other, (1 mark) What is the proballity exactly 2 tests out of the 10 give a positive test indicating that corrosion is present? (4 dp):