Consider a continuous-time Markov chain with three states 1, 2, 3, 4, 5 and transition rates 912 = 1,913 = 2, 921 =0, 923 = 3, - 931 = 0, 932 = 0. (1) Write the system of ODEs for the corresponding transition probabilities P (t). [10 points] (2) Suppose that the initial state is 1. What is the probability that after the first transition, the process (t) enters state 2? [8 points]