Solving problem N3850 Bayesian probability theory

Solving problem N3850 Bayesian probability theory

3850. 70% of the parts entering the assembly are made by an automatic machine giving 2% of scrap, and the remaining parts are made by an automatic machine giving 5% of scrap. 1) What is the probability that a randomly selected item was defective? 2) It is known that the part taken at random turned out to be defective. On which machine was this part most likely produced?

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