In a war, there are three surviving tanks A,B, and C. Tank A can hit its target

Question

In a war, there are three surviving tanks A,B, and C. Tank A can hit its target with probability 1/3; tank B with probability 1/4; and tank C with probability 1/5. In a fight, they shoot simultaneously and randomly pick one of the other surviving tanks as a target. Show that, after the first round,
a. PR{no tank survives} = 1/240
b.PR{all tanks survives} = 24/60
c PR{Only tank A survives} = PR{Only tank B survives}=PR{Only tank C survives}=1/24
d.PR{A and B survive}=11/60
e.PR{B and C survive} = 1/8
f. PR{A and C survive}=39/240

Explanation / Answer

C

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