Solving problem N3714 Bayesian probability theory

Solving problem N3714 Bayesian probability theory

3714. Two punchers stuffed on different punchers on the same set of punched cards. The probability that the first puncher makes a mistake is 0.05; for the second puncher, this probability is 0.1. An error was found when checking the punched cards. Find the probability that the first puncher made a mistake. (It is assumed that both perforators were intact.)

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Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)