1.Two aristocrats fight a duel.Each has a pistol loaded with 1 bullet.They start 10 steps a part and walk towards each other at an identical rate of one step per second. After each step either may fire the gun. After k steps the probability of scoring a hit is k/5 for each player.If you fire and miss, you must keep walking to face certain death after five steps.Each player gets a payoff of -1 if they get killed and 1 if they kill their opponent. If neither or both are killed each gets 0.

a)Draw a game diagram and label it.

b)Solve the game

c)Repeat the game if one player has a probability of k/10 of scoring for one player (she has a vision problem).