Solution of problem N1414 Laplace probability theory

Solution of problem N1414 Laplace probability theory

1414. The die is thrown 120 times. Find the probability that:
a) the "five" will fall 20 times;
b) the "five" will drop from 10 to 30 times.
Find approximate the boundaries in which the number of occurrences of the "five" will be enclosed with a probability of 0.9973.

Additional information:

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