Solution of problem N3842 probability theory total prob

Solution of problem N3842 probability theory total prob

3842. There are three batches of radio tubes, numbering respectively 40, 40 and 20 pieces. The probabilities that the radio tube will work for a given time are equal, respectively, for these batches to 0.5; 0.7 and 0.8. Find the probability that a selected lamp of 100 will work at random for a given time.

Additional information:

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