Solution of problem N3963 probability theory total prob

Solution of problem N3963 probability theory total prob

3963. The store received electric bulbs produced by two plants. Among them, 70% are made by the 1st plant, and the rest - by the 2nd. It is known that 3% of the lamps of the 1st plant and 5% of the lamps of the 2nd plant do not meet the standard. What is the probability that a lamp taken at random will be standard?

Additional information:

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