A manufacturer has two machines that make the same parts for diesel truck engines. One machine is 5 years older than the other one. The older machine runs slower and makes 35% of the parts, of which 85% are of acceptable quality and don't require rework. Only 8% of the parts made by the newer machine require rework?
If a part is found to be out of specification and in need of rework, what is the probability that is was made by the older machine?