Question

Suppose we are interested in surveying the problematic water pipes in New York City. It is known that 10% of the NYC water pipes have some problems. City officials develop a non-intrusive test machine to scan the underground pipes. The machine correctly identifies 95% of the problematic sites (i.e. the machine says the pipe has a problem for a site that in fact has an issue), but it wrongly identifies 5% of the sites as problematic (i.e. machine says the pipe has a problem for a site that does not have an issue with the probability of 5%). What is the probability that a site has no problem when the machine says that the pipe at the site has no issue

Answer 1

The probability that a site has no problem when the machine says that the pipe at the site has no issue is

0.905

Explanation:

Confidence level = 95%

Error level = 5% (1 - 95%)

Since the probability that the machine says the pipe has a problem for a site that in fact has an issue = 95% and the pipe has a problem in 10% of the case, this means that the pipe has a problem in exactly 0.095 (10% * 95%).

Therefore, the probability that a site has no problem when the machine says that the pipe at the site has no issue = 0.905 (1 - 0.095).