(15 pts) A quality characteristic is monitored by a control chart designed so the probability that a certain out of control condition will be detected on the rst sample following the shift to that state is 1 6. (a) What is the probability that the out of control state will be detected on the second sample following the shift. (b) What is the probability that the out of control state will be detected on the mth sample following the shift. (c) What is the probability that the rst point following the shift lies within the control limits