Solution of problem N3861 probability theory total prob

Solution of problem N3861 probability theory total prob

3861. The assembler received 6 boxes of parts manufactured by plant No. 1 and 4 boxes of parts manufactured by plant No. 2. The probability that a part of factory number 1 is standard is 0.8, and that of factory number 2 is 0.75. The collector picked up the item at random from the box taken at random. Find the probability that the defective part is extracted.

Additional information:

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