... be used to detect corrosion (C), excessive deflection (D) and clogging (G). The makers of the test claim that it can detect corrosion with 99% accuracy, excessive deflection with 98% accuracy and clogging with 90% accuracy. If any one of the above defects is present the test signals (S), otherwise it will not signal. Based on actual data corrosion is present in 50% of pipes, excessive deflection in 35% of the pipes and clogging in 15% of the pipes. If a pipe is selected randomly:
(a) What is the probability that the test will signal?
(b) If the test signals what is the probability that there was excessive deflection?