Answer all questions with explanation

The following is the transition probability matrix of a Markov chain with states 1,2,3,4 P = (0.4 0.2 0.3 0.1) (0.2 0.2 0.2 0.4) (0.25 0.25 0.5 0) (0.2 0.1 0.4 0.3) (a) find the probability that state 3 is entered before state 4; If X0 = 1 (b) find the mean number of transitions until either state 3 or state 4 is entered