Q. By the rule of seven, a process is said to be out of control if a run of seven samples is found on one side of the process mean. What is the probability that a run of seven occurs on either side of the mean due to random variation?
Answer (c) 1.56% . Correct Answer is 'C'. Let the first sample be on any one side of the mean. The probability that the subsequent sample is on the same side is A, the probability that the third sample is on the same side is again 1/2 A, and so on. The probability for the seventh sample on the same side is also A. Therefore the probability that all the six subsequent points is on the same side as the first is 1/2A * 1/2A * 1/2A * 1/2A * 1/2A * 1/2A = 1/64 = 0.0156 => 1.56%.
Can anybody explain why are we not taking 1/2*1/2*1/2*1/2*1/2*1/2*1/2=1/128?