Consider a company specialising in engineering devices for use in nuclear power plants. Suppose one of the products they produce is a Geiger counter. Each Geiger counter the company produces is tested prior to dispatch, to ensure it is not defective. Let D denote the event that a Geiger counter produced by the company is truly defective, and let F denote the event that a Geiger counter is labelled as being defective, due to failing the rigorous internal quality control test. Based on past audits, it is known that 1% of all Geiger counters produced by the company are defective. It is also known that the quality control test can correctly detect these defective Geiger counters with a probability of 0.81. Further, it is known that non-defective Geiger counters (i.e. properly functioning Geiger counters) can fail the quality control test with a probability of 0.19. Use this information to answer the following questions. For parts e, f and g, round your answers to three decimal places. a. What is P(D)? (1 mark) 4 b. What is P(DC)? (1 mark) c. What is P(F D)? (1 mark) d. What is P( F DC)? (1 mark) e. What is the probability that a Geiger counter fails the quality control test? (3 marks) f. Suppose that a Geiger counter fails the quality control test. Then what is the probability that it is not truly defective? (3 marks) g. Given that a Geiger counter fails the quality control test, what is the probability that it is truly defective? (2 marks)