Solution of problem N3889 probability theory total prob

Solution of problem N3889 probability theory total prob

3889. The collector receives an average of 50% of parts from plant number 1, 30% from plant number 2, 20% from plant number 3. The probability that the part from factory number 1 of excellent quality is 0.9, for factory number 2 and number 3, these probabilities are equal to 0.6 and 0.9, respectively. Find the probability that the item extracted for good luck will be of excellent quality.

Additional information:

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