please consider this question:
A study using Markov chains to estimate a patient's prognosis for improving under various treatment plans gives the following transition matrix as an example
a) Estimate the probability that a well person will eventually end up dead.
b) Find the expected number of cycles that a well patient will continue to be well before dying, and the expected number of cycles that a well patient will be ill before dying.
Sorry I'm new to Markov chains and please help me solve this question
Assume the guy starts out healthy. You need to construct a recurrent equation for the 3-state MC with 1 absorbing state: $$ h_{1,3}=0.3 h_{1,3} +0.5 h_{2,3} +0.2 h_{3,3}\\ h_{2,3}=0.5 h_{2,3}+0.5 h_{3,3} $$ Keep in mind $h_{3,3}=1$ (obviously). Solve for $h_{1,3}$. For the second problems use Geometric probability.