3837. There are three batches of radio tubes, respectively, 50, 20 and 30 pieces. The probabilities that the radio tube will work for a given time are equal, respectively, for these batches to 0.8; 0.9 and 0.5. Find the probability that a selected lamp of 100 will work at random for a given time.

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