Solution of problem N3891 probability theory total prob

Solution of problem N3891 probability theory total prob

3891. The collector receives 30% of parts manufactured at plant number 1; 20% - at the plant number 2; the rest - at the factory number 3. The probability that a part of factory number 1 is of excellent quality is 0.9; this probability for plant number 2 is 0.8; for plant number 3 - 0.6. Find the probability that an item randomly picked by the collector is of excellent quality.

Additional information:

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