3955. The light bulbs of three plants come into the store. The first plant produces 45% of all products, the second 40% and the third 15%. The production of the first plant contains 70% of standard lamps, the second 80%, the third 81%. The lamp purchased in the store turned out to be standard. What is the probability that it is made at the first plant?

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