3835. There are three batches of lamps of 25, 30, 45 pieces each, respectively. The probability that the lamps will work for a given time is equal for each batch of 0.7, 0.8 and 0.9, respectively. What is the probability that a lamp chosen at random from a hundred of these lamps will work for a specified time?

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