3857. The assembler received 3 boxes of parts manufactured by plant No. 1, and 2 boxes of parts manufactured by plant No. 2. The probability that part of plant No. 1 is standard is 0.8, and that of plant No. 2 is 0.9. The collector picked up the item at random from the box taken at random. Find the probability that the standard part is extracted.

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