Solving problem N3950 Bayesian probability theory

Solving problem N3950 Bayesian probability theory

3950. Electric bulbs are manufactured at 3 plants. The first plant produces 45% of the total number of light bulbs, the second - 40%, the third - 15%. The production of the first plant contains 70% of standard lamps, the second - 80%, the third - 85. The products of all three factories enter the stores.
1) What is the probability that a lamp purchased at the store will be standard?
2) What is the probability that the lamp is made at the second plant, if it is known that it is standard?

Additional information:

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