Question

Engineers in charge of maintaining our nuclear fleet must continually check for corrosion inside the pipes that are part of the cooling systems. The inside condition of the pipes cannot be observed directly but a nondestructive test can give an indication of possible corrosion. This test is not infallible. The test has probability 0.7 of detecting corrosion when it is present but it also has a probability 0.2 of falsely indicating internal corrosion. Suppose the probability that any section of pipe has internal corrosion is 0.1. What is the probability that a section of pipe has corrosion giv

Answer 1

@nabeeltariq Can you please post the missing last part of the question.

Answer 2

This sentence is not finished in your question:
"What is the probability that a section of pipe has corrosion giv "

Answer 3

What is the probability that a section of pipe has corrosion given that the test is negative?

Answer 4

What is the probability that a section of pipe has corrosion given that the test is negative?

Answer 5

P(true positive) = 0.1 * 0.7 = 0.07
P(false negative) = 0.1 * 0.3) = 0.03
P(false positive) = 0.9 * 0.2) = 0.18
P(true negative) = 0.9 * 0.8) = 0.72
P(test is negative) = 0.03 + 0.72 = 0.75
The probability that a section of pipe has corrosion given that the test is negative is :
\[\frac{0.07}{0.75}=0.093\]