In a war, there are 3 surviving tanks, A, B and C. Tank A can hit its target with probability 1/3, tank B with probability 1/4 and tank C with probability 1/5. In a fight, they repeatedly fire simultaneously until either only one tanks survives or none. Assume a surviving tank randomly picks one of the other surviving tanks as a target. Let X, be the tank(s) that still survive the fight at shot number n. Find (a) The state space S. (b) The transition matrix of {X, }n=0,1,2,... (c) The expected duration of the entire fight. (d) The probability that none survives after the fight. (e) The probability that only tank A survives after the fight, only tank B survives, and only tank C survives. In a war, there are 3 surviving tanks, A, B and C. Tank A can hit its target with probability 1/3, tank B with probability 1/4 and tank C with probability 1/5. In a fight, they repeatedly fire simultaneously until either only one tanks survives or none. Assume a surviving tank randomly picks one of the other surviving tanks as a target. Let X, be the tank(s) that still survive the fight at shot number n. Find (a) The state space S. (b) The transition matrix of {X, }n=0,1,2,... (c) The expected duration of the entire fight. (d) The probability that none survives after the fight. (e) The probability that only tank A survives after the fight, only tank B survives, and only tank C survives