7 Suppose that each engine can be inspected before the flight. After inspection, each engine is labeled as being in either good or bad condition. You are given that P(inspection says engine is in good condition | engine will fail)  .001 P(inspection says engine is in bad condition | engine will fail)  .999 P(inspection says engine is in good condition | engine will not fail)  .995 P(inspection says engine is in bad condition | engine will not fail)  .005 a If the inspection indicates the engine is in bad condition, what is the probability that the engine will fail on the flight?

b If an inspector randomly inspects an engine (that is, with probability .001 she chooses an engine that is about to fail, and with probability .999 she chooses an engine that is not about to fail), what is the probability that she will make an error in her evaluation of the engine?