Solution of problem N3766 probability theory total prob

Solution of problem N3766 probability theory total prob

3766. The assembly received parts made on two machines, with 60% of all parts coming from the first machine, of which 80% of parts of the 1st grade and 70% of the parts of the first grade from the second machine. What is the probability that the item taken will be of the first grade?

Additional information:

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