Solution of problem N1442 Bernoulli probability theory

Solution of problem N1442 Bernoulli probability theory

1442. There are four electric bulbs in the apartment. For each bulb the probability that it will remain intact for a year is 5/6. What is the probability of having to replace at least half of the bulbs during the year?

Additional information:

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