Solving problem N3905 Bayesian probability theory

Solving problem N3905 Bayesian probability theory

3905. At the enterprise manufacturing the locks, the first workshop produces 20%; the second is 50%; third is 30%. Defective products for these workshops are respectively 5%, 4%, 2%. a) find the probability that a randomly selected lock will be defective. b) a randomly selected lock turned out to be defective. Most likely, in what shop it is made?

Additional information:

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