  If a Markov chain is the correct model of a process, then even when the individual trial outcomes happen by chance, we should expect the entire sequence of repeated trials to be non-random. In the weather case just discussed, we should expect a sunny day to be followed by a sunny day, and a rainy day by a rainy one. In our notation 11 and 00 should be more frequent than 10 or 01. But the condition of Borel normality, which all random sequences obey, entails that every finite sequence of outcomes of equal length should have equal frequency in the sequence. So no Borel normal sequence, and hence no random sequence, can model the sequence of outcomes of a Markov chain, even though each outcome happens by chance.