Solution of problem N3835 probability theory total prob

Solution of problem N3835 probability theory total prob

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?

Additional information:

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