Solution of problem N2599 probability theory

Solution of problem N2599 probability theory

2599. At one factory for every 100 light bulbs there are on average 15 non-standard ones, on the second - 10, and on the third - 25. The production of these plants is 30; 45 and 25% of all light bulbs purchased by residents of the area.
a) Find the probability that the acquired light bulb will be standard.
b) The light bulb turned out to be standard. What is the probability that this light bulb is made at the first factory?

Additional information:

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