Going case by case and Taking into consideration Daves suggestion that A
will prefer to kill B if all three are alive and B will prefer to kill C if
all three are alive, We find the following probabilities of survival of C by
starting.
P(when C shoots at B)=2/9
P(when C shoots at A)=13/36
P(when C shoots in air)=5/12

Hence C must chose to shoot in air.

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