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.

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