Analysis of historical data shows the probability a machine tool your company produces will fail when installed in a customer’s factory is 0.02. Your quality assurance department utilizes sophisticated testing and diagnostic equipment to determine whether a machine tool you produce will function once it is installed in a customer’s factory. If the machine tool would function when installed, the probability that quality assurance department testing would indicate the machine tool will fail when installed is 0.05. If the machine tool will fail when installed, the probability that quality assurance testing will indicate the machine tool will fail is 0.99.
F+ = Machine functions when installed
F- = Machine will not function when installed
T+ = QC Test indicates machine will function
T- = QC Test indicates machine will not function
Required:
(a) What is the probability that the machine tool WILL function when installed given the quality assurance testing indicates the machine tool WILL function?
(b) What is the probability that the machine tool WILL function when installed given the quality assurance testing indicates the machine tool will NOT function?
(c) What is the probability that the QC Test indicates the machine WILL NOT function?
(d) What is the probability that quality assurance department testing would indicate the machine tool will function when installed if, in fact, it does not function when installed?