Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2013 / Paper 1 / 18 / b / Solution

Let $A,B,C$ denote the mutually exclusive supplier events and $D$ the defective-bulb event. Their probabilities and conditional defect rates areThese supplier events partition the possible bulbs. The following calculations use the law of total probability and Bayes' theorem with that partition.