A truel is like a duel except there are three players involved. We will call them player A, player B, and Player C. Each player comes with his...

A truel is like a duel except there are three players involved. We will call them player A, player B, and Player C. Each player comes with his probability of hitting a target. Player A hits a target with probability pA=0.70, Player B with probability pB=0.60 and Player C with probability pC=0.1. The game is played by rounds. At each round the players shoot at each other simultaneously, hence their speed doesn't matter. The truel is over when ONLY ONE player is still alive or if all three of them are dead. We assumed that each player has infinitely many bullets.

For the truel, use the following strategy: A shoots at B, B shoots at A, C shoots at A.

Question: Create a Markov Chain to solve this problem.

(a)  First list all states.

(b)  Second make a connections and determine the probabilities. Create a Markov diagram (graph).

(c)  Determine all absorbing states.

(d)  Create transition Matrix.

(e)  Compute the winning probabilities for all players as well as probability that no one survives.

(f) Compute the expected number of rounds for the whole truel using a pdf table which is used to compute expectation