In a combat b/n 3 persons A, B, C the probabilities of A, B, C shooting at the target are 0.3, 0.5, 1. They will get the gun in the order A, B, C, A, B, C .... Every person targets to hit the relatively dangerous person and the combat continues until one person is left unhit. Then probability that A is left unhit. (If a person is lit, he is out of combat)
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i) If A hits C then,
= (0.3) (0.5) [P 1 + P 3 + P 5 + .........
= (0.15) [0.3 + (0.7) (0.5) (0.3) + ........]
= (0.15) 
ii) If A does not hit C,
= (0.7) [(0.5) (P 1 + P 3 + P 5 + .....) + 0.3 x 0.5]
= 0.35 
Required probability = 
.
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