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**Soroban** Three men $\displaystyle \{A,B,C\}$ decide to settle their dispute with a duel.

They stand at the vertices of a large equilateral triangle

and will take turns shooting at each other.

They draw lots to determine who gets to shoot first, second and third.

At his turn, each man gets to shoot at one other man.

$\displaystyle A$ always hits his target.

$\displaystyle B$ hits his target with probability 4/5.

$\displaystyle C$ hits his target with probability 3/5.

(a) Find the probability of each man's survival.

(b) Who has the best chance for survival?

Note: These men are highly intelligent.

. . . . .They will select their targets with great care.