Solving problem N3906 Bayesian probability theory

Solving problem N3906 Bayesian probability theory

3906. At the company that manufactures the locks, the first workshop produces 25%, the second - 35%, the third - 40% of all locks. Marriage is 5%, 4% and 2% respectively. Find the probability that: a) a randomly selected lock is defective; b) this defective lock was made in the third workshop.

Additional information:

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