Solving problem N3928 Bayesian probability theory

Solving problem N3928 Bayesian probability theory

3928. Two plants produce refrigerators of the same brand, with the first plant producing twice as much as the second. The first plant produces on average 70% of top-quality refrigerators, and the second 80%. The refrigerator chosen at random turned out to be top notch. Find the probability that the refrigerator is made at the first factory.

Additional information:

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