expected range probability

I'd need help in solving the following probability theory / AI question. The result of an industrial process can be described as a time series X = (X1, X2, ...Xn). The probability distribution of X is unknown. There is given a Th << Xn threshold value. An Xi element of the time series is in the expected range if (Xn+Th) >= Xi >= (Xn-Th). What is the probability of the event, when at least one of the next k elements ( k << n ) of the time series is out of the expected range? I'd like to get detailed explanation for the solution.