Solving problem N3958 Bayesian probability theory

Solving problem N3958 Bayesian probability theory

3958. Electric bulbs are manufactured in two factories, the first producing 60% of the total, the second 40%. The production of the first plant contains 70% of the lamps of the highest grade, the second - 80%. The store receives products from two factories. The purchased lamp was not the highest grade. Find the probability that this lamp is made at the first factory.

Additional information:

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