Solving problem N4026 Bayesian probability theory

Solving problem N4026 Bayesian probability theory

4026. The same type of products come from three factories to the store, with the 1st plant supplying 60% of the products, the 2nd plant - 10%, the 3rd plant - 30%. Among the products of the 1st plant 80% are first-class, among the products of the 2nd - 90%, of the 3rd - 80%. Bought one product. It turned out to be first-rate. Determine the probability that the purchased product is produced by the 1st plant.

Additional information:

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