Consider Problem 16-4.

(a) For a patient who is currently on dialysis, what is the probability of receiving a transplant in 2 years?

(b) For a patient who is currently a more-than-1-year survivor, what is the probability of surviving 4 more years?

Problem 16-4

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