One ofthe assumptions underlying the theory ofcontrol charting is that successiye plotted points are independent of one another. Each plotted point can signal either that a manufacturing process is operating correctly or that there is some sort of malfunction. Eyen when a process is running correctly, there is a small probability that a particular point will signal a problem with the process. Suppose that this probability is [1.06. IWhat is the probability that at least one of 10 successiye points indicates a problem when in fact the process is operating correctly? {Round your answer to three decimal places.) |:| IWhat is the probability that at least one of 15 successiye points indicates a problem when in fact the process is operating correctly? {Round your answer to three decimal places.) E Consider purchasing a system of audio components consisting of a receiyer. a pair of speakers. and a CD player. Let}!1 be the event that the receiver functions properly throughout the warranty period, A2 be the event that the speakers function properly throughout the warranty period, and A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are [mutually] independent with PHI] = [1.93. PEAR] = [1.92, and PEAS] = 0.?0. {Round your answers to four decimal places.) {a} What is the probability that all three components function properly throughout the warranty period? |:| [b] What is the probability that at least one component needs service during the warranty period? |:| [c] What is the probability that all three components need service during the warranty period? |:| [d] What is the probability that only the receiyer needs service during the warranty period? |:| {e} What is the probability that exactly one ofthe three components needs service during the warranty period