Solution of problem N3899 probability theory total prob

Solution of problem N3899 probability theory total prob

3899. Three automatic machines of various brands produce parts. The performance of the 1st machine per shift is 40 parts, the 2nd - 35 parts, the 3rd - 25 parts. It is established that 2, 3 and 5% of the products of these machines have latent defects, respectively. At the end of the shift, one part was taken for control. Find the probability that this part is non-standard.

Additional information:

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