Solution of problem N1931 Laplace probability theory

Solution of problem N1931 Laplace probability theory

1931. The device consists of 80 elements with the same reliability of 0.8 (reliability of the element - the probability of its operation in time t). Elements fail regardless of each other. Find the probability that:
1) within a time t, from 10 to 20 elements will fail;
2) the relative failure rate of elements will deviate from the probability of this event by less than 0.1 (in absolute value).

Additional information:

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