Solving problem N3645 Bayesian probability theory

Solving problem N3645 Bayesian probability theory

3645. The QC controller receives products made by four workers. A total of 200 items arrived; of them: 10% made the first worker; 25% - the second; 15% - the third. The probability of marriage for the first worker is 0.1; the second is 0.2; the third - 0.15; fourth - 0.25. At random, the chosen product turned out to be without marriage. What is the probability that it is manufactured by the first worker?

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