Hamsters at a pet shop can either be Healthy (State 0), Injured (State 1), or Dead (State 2). Hamsters can transition both ways between State 0 and State 1 , but cannot move out of State 2 once in that state. You are given the following constant forces of transition:

(i) 01 = 0.03 (ii) 10 = 0.08 (iii) 02 = 0.01 (iv) 12 = 0.09

Calculate the probability that an injured hamster on Jan 1, 2012 will become healthy before the end of the year, but will not remain continuously healthy until the end of the year.