In Exercise 2 , suppose that if it has rained for the past three days, then it will rain today with probability $0.8 ;$ if it did not rain for any of the past three days, then it will rain today with probability $0.2$; and in any other case the weather today will, with probability $0.6$, be the same as the weather yesterday. Determine $\mathbf{P}$ for this Markov chain.