At any given time, a subatomic particle can be in one of two states, and it moves randomly from one state to another when it is excited on one observation, then it is 2 times as likely to be in state 1 as state 2 on the next observation. Likewise, if it is in the state 2 on one s 2 as likely to be in the state 2 as state 1 on the next observation. 1. Find the transition matrix for this Markov chain. 2. If the particle is in state 1 on the first observation, what is the probability it is in state 1 on the fourth observation?

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