Solving problem N3988 Bayesian probability theory

Solving problem N3988 Bayesian probability theory

3988. The store received, respectively, 20, 15 and 10 coats of three different firms. It is known that the share of high-quality products among the products of the first company is on average 70%, the second 80% and the third 60%. At random, the chosen coat was bad. Find the probability that it is supplied by the second firm.

Additional information:

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