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Who will have the highest chances for surviving in the truel and how much is the chance?

+1 vote

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?

posted Aug 31, 2015 by Vishal

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1 Answer

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B has the highest change: 43%
C has 40% and A 17%
If A starts, he will kill B. C will have 50%, thus A survives 50% and C the other 50%
If B starts, he will kill A. C will have 50%, thus B survives 50% and C the other 50%
If C starts, he will kill A. B has 80% chance to hit, thus B survives 80% and C the other 20%.
As each of these three options have a 1/3 chance of occurring, the survival rate is:
A: 50% * 1/3 = 17%
B: 50% * 1/3 + 80% * 1/3 = 43%
C: 50% * 1/3 + 50% * 1/3 + 20% * 1/3 = 40%

answer Sep 1, 2015 by Jcm

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