Solution of problem N1670 Laplace probability theory

Solution of problem N1670 Laplace probability theory

1670. The probability of hitting one shot from this type of weapon is 0.4. A series of 40 shots (independent of each other) is held. Find the probability that there will be 10 to 20 hits. How many shots should be fired so that the probability of deviating the relative hit frequency from the probability of hit by less than 0.05 is 0.9 (in absolute value).

Additional information:

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