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An artillery target may be either at poi...

An artillery target may be either at point A with probability `(8)/(9)` or at point B with probability `(1)/(9)`, we have 21 shells, each of which can be fired either at point A or at point B. Each shell may hit the target independently of the other shells, with probability `(1)/(2)` How may shells must be fired at point A to hit the target with maximum probability ?

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