Solution of problem N3853 probability theory total prob

Solution of problem N3853 probability theory total prob

3853. The assembly receives gears from three machines. The first machine gives 15%, the second - 45%, the third - 40% of gears arriving at the assembly. The first automatic machine allows 0.2% of gears to fail, the second - 0.3%, the third - 0.4%. Find the probability of receipt of the assembly of defective gear.

Additional information:

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