Solution of problem N3735 probability theory total prob

Solution of problem N3735 probability theory total prob

3735. The assembly shop received parts from three machines. The first machine made 80% of the parts of their total number, the second machine 10% and the third 10%. In this case, the first machine tool produced 90% of the first-class parts, 80% in the second and 70% in the third. Using the formula of the total probability to determine what is the probability that the item taken at random will be of the first grade?

Additional information:

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