A production line has a detection system that is designed to detect flaws in the early phases of the manufacturing process. These flaws can cause the entire production line to break down from 12 to 24 hours, causing a significant loss. A reliability question deals with the ability of the system to identify a defect and issue a warning for it to be immediately fixed or removed. Assume that a particular detection system has 80% probability of detecting a flaw. Answer the following questions using the binomial probability distribution: You may use an online probability calculator or scientific calculator, but you must demonstrate all other calculations in order to earn full points on the questions below, and you must write down the meaning of the result you calculated in full sentences. a) What is the probability that one detection system will detect a flaw? (5 points) b) If two detection systems are installed in the same production line and operate independently, what is the probability that at least one of the systems will detect a flaw? (5 points) c) If three systems are installed, what is the probability that at least one of the systems will detect a flaw? (5 points) d) Calculate the probability for n=3 and P (at least 2 systems will detect a flaw). Explain and interpret the result. (5 points) a) Would you recommend that multiple detection systems be operated? Fully justify your answer. (5 points)