A physical device can be in three states: A, B, C. The device operates as follows (all time units are in hours): . The device spends an exponentially distributed amount of time in state A (with mean of 12 minutes) and then with probability 0.6 goes to state B, and with prob. 0.4 goes to state C. . When in state B, the device moves to state C after an Exp(3) amount of time. . When in state C, the device goes to state A at rate 1/hour, and to state B at rate 2/hour. Let X, represent the device state at time t, and suppose Xo = 'A'. Compute: 1. Probability the device is in state 'A' after 30 minutes. 2. Probability the device is in state 'A' after 30 minutes given that it was in state 'B' after 5 minutes and in state 'C' after 10 minutes. 3. The long-run proportion of time the device spends in state 'A'