Finding probability from a markov chain

label Mathematics
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this chain has a transition matrix of:

.4 .6

.8 .2

If, on the first observation, the system is in state 2, what state is the system most likely to occupy on the third observation? (If there is more than one such state, which is the first one.) 

Apr 20th, 2015

2nd:  P(s1) = 0.8 P(S2) = 0.2 

3nd P(S1) = 0.4*0.8 +0.8*0.2 = 0.32+0.16 = 0.48

P(S2) = 0.6*0.8+0.2*0.2 = 0.52

so it is state 2 

Apr 20th, 2015

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Apr 20th, 2015
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Apr 20th, 2015
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