According tothis Wikipedia article:

• Sensitivitymeasures the proportion ofpositivesthat are correctly identified (e.g. the percentage of a certain product that is correctly identified as having a defect)
• Specificitymeasures the proportion ofnegativesthat are correctly identified (e.g. the percentage of a certain product that is correctly identified asnothaving a defect)

Suppose we are interested in surveying the problematic water pipes in New York City. Unknown to us, 10% of the NYC water pipes have some problems. City officials develop a non-intrusivetest to scan the underground pipeswith 95% sensitivity and 90% specificity.

What is the probability that this test gives a positive (i.e. the test says that surveyed location has a problem)? Explain your answer.