markov chain sequence

In  markov chain you have a transition matrix and initial state.

It is easy to work out the probability on the nth event but what about a sequence of events .

the 1st column .75 is prob a day is wet today given it was wet yesterday .
the 1st column .7 is prob a day is not wet given it was not wet yesterday .

 t= .75  .3
     .25  .7  

what is the probability of a at least 2 days being wet out of the next 3 if it was wet yesterday.

using a markov chain how do i do this?
jagguyAsked:
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TommySzalapskiCommented:
Start from the state of it was wet yesterday and then work out all the possible final states for the next 3 days (you should have 8 of them). Now find the paths that have 2 or more wet days and add up the probabilities.
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ozoCommented:
P(W|W)*P(W|W)
+
P(D|W)*P(W|D)*P(W|W)
0
d-glitchCommented:
This is a three level tree with eight possible outcomes.
You care about four of them.
0
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ozoCommented:
P(W|W)*P(W|W)
+
P(W|W)*P(D|W)*P(W|D)
+
P(D|W)*P(W|D)*P(W|W)
=
P(W|W)*P(W|W) + 2*P(D|W)*P(W|D)*P(W|W)
=
P(W|W) * (P(W|W)+2*P(D|W)*P(W|D))
0

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jagguyAuthor Commented:
ok so what is the answer and the s0 matrix as it goes along?
0
TommySzalapskiCommented:
You know that we can't just solve the whole problem for you. This is an academic question.

What do you have for it so far?
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