Solving problem N3942 Bayesian probability theory

Solving problem N3942 Bayesian probability theory

3942. The watches entering the store are manufactured at three factories. The first plant produces 40% of products, the second - 45%, the third - 15%. In the production of the first plant, 80% of the hours are in a hurry, the second - 70%, the third - 90%.
1. What is the probability that a watch purchased at random is in a hurry?
2. It is known that the watches bought at random are in a hurry. Find the probability that they are produced at the first plant.

Additional information:

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