It costs ($ 50) to find out whether a spare part required for repairing a failed device

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It costs \(\$ 50\) to find out whether a spare part required for repairing a failed device is faulty or not. Installing a faulty spare part causes damage of \(\$ 1000\).

Is it on average more profitable to use a spare part without checking if

(1) \(1 \%\) of all spare parts of that type,

(2) \(3 \%\) of all spare parts of that type, and

(3) \(10 \%\) of all spare parts of that type are faulty?

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