Solving problem N3719 Bayesian probability theory

Solving problem N3719 Bayesian probability theory

3719. Two operators stuffed on different punchers on the same set of punched cards. The probability that the first operator makes a mistake is 0.1; for the second operator, this probability is 0.2. An error was found when checking the punched cards. What is the probability that the second statement was wrong?

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