Patients suffering from kidney failure can either get a transplant or undergo periodic dialysis. During any 1 year, 25% undergo cadaveric transplants, and 12% receive living-donor kidneys. In the year following a transplant, 20% of the cadaveric transplants and 10% of living-donor recipients go back to dialysis. Death percentages among the two groups are 30% and 16%, respectively. Of those in the dialysis pool, 15% die, and of those who survive more than one year after transplant, 4% die and 5% go back to dialysis.

1. Represent the situation as a Markov chain.
2. For a patient who is currently on dialysis, what is the probability of receiving a transplant in 2 years?
3. For a patient who is currently on dialysis, what is the probability of them dying in 3 years?
4. For a patient that is currently more-than-one-year survivor, what is the probability of surviving 3 more years?