Once upon a time there were three rivals who got together in a dark wood on an open spot for composing a quarrel by using guns. It was a kind of duel but there were three people in it and therefore it is a truel. There were A, B and C. there was some rules to be followed in the game. The rules of the games were:
-They have to draw the lots in order to find who will fire first and who will be second and who will be third.
- The next rule is that, they will start firing on each other unless there is a last person alive.
- Each person will decide on his own about which person he will fire on.
-it is quite clear that A hits and kills in all the shots and it is 100%. Whereas 80% of the shots are hit by B and C hits in 50% of the shots he tries to fire in. the three persons have their own strategy for firing. Nobody is killed by the stray bullet.
Question: who will have the highest chances for surviving in the truel and how much is the chance?
the person C will have the highest chances of survival.
Person A hits = 1
Person A misses = 0
Person B hits = 4/5
Person B misses = 1/5
Person C hits = 1/2
Person C misses = 1/2