During a turbine airfoil manufacturing operation, rows of cooling holes are drilled by a laser. Suppose three different laser drilling machines are used to drill 30%, 45% and 25% of the airfoils, respectively. The airfoils are inspected for quality after the drilling operation by a flow bench, and if the measured flow rate does not fall within specification limits, it is rejected. Given past experience with these machines, the company has learned the percentages of airfoils that fail to pass inspection. The quality rejection rate from each machine is known to be 2%, 3% and 2%, respectively. Suppose a finished airfoil is selected randomly from a large batch from all three machines.
a) What is the probability that the airfoil will fail a flow inspection?
b) Determine the probabilities that a rejected airfoil is from each of the three machines?
c) Draw a tree diagram of the manufacturing and inspection process.