Final answer:
To determine the most likely steady state condition of the system, we can use the concept of a Markov chain and solve a system of balance equations.
Step-by-step explanation:
In this problem, we are given the probabilities of processing a command without receiving a new command and receiving a new command without completing a command. We need to determine the most likely steady state condition of the system, which refers to the number of commands in the stack.
To solve this problem, we can make use of the concept of a Markov chain. In a Markov chain, the steady state condition refers to the long-term behavior of the system when it reaches equilibrium.
The most likely steady state condition of the system can be determined by finding the distribution of commands in the stack. This distribution can be obtained by solving a system of linear equations, known as the balance equations.
In this case, since the maximum number of commands the stack can hold is 9, there are 10 possible states for the system (0 commands in the stack to 9 commands in the stack).
By solving the balance equations, we can determine the probabilities of having each number of commands in the stack in the long run. The most likely steady state condition of the system is the one with the highest probability.