Three machines operate together on a manufacturing floor, and each day there is a possibility that any of the machines may fail. The probability of their failure depends upon how many other machines...

Three machines operate together on a manufacturing floor, and each day there is a possibility that any of the machines may fail. The probability of their failure depends upon how many other machines are still in operation. The number of machines in operation at the beginning of each day is represented by the state values of 0,1,2,3 and the corresponding state transition probability matrix is First explain why P has zero entries. Next determine how many days will pass before the probability of all 3 machines failing is greater than 0.8. Assume that intially all 3 machines are working. Hint: You will need a computer to find the solution.