Solution of problem N3857 probability theory total prob

Solution of problem N3857 probability theory total prob

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.

Additional information:

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