@Dave: Sorry It was a typo but for the probability figures,
When C shoots B then if he is successful then A will shoot C
Hence he must be unsuccessful and then
if B is unsuccessful then A must will Kill B and then C must kill A
if B is successful then C must kill B now
Hence P(when C shoots at B)=(2/3 )*( (1/2)*(1/3) + (1/2)*(1/3) )
=2/9

When C shoots at A i am similarly getting for the case when A is killed as
1/12
and when A is safe as 5/18
Hence total 13/36

where am i wrong?

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