Solution of problem N1178 Laplace probability theory

Solution of problem N1178 Laplace probability theory

1178. There are 80 white and 20 black balls in the urn. How many balls (with return) need to be removed from the urn so that with a probability of 0.95 one could expect that the frequency of the appearance of the white ball will deviate from the probability by less than 0.1?

Additional information:

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