MathDB

The accuracy of a mystic's prediction is related to the volume of his or her crystal ball by the equation

P = 1 - (0.999)^V

, where

P

is the probability the mystic's prediction is correct and

V

is the volume of his ball in cubic centimeters. These crystal balls are sold wth radii that are a whole number of centimeters. What is the radius (in centimeters) of the smallest ball that gives the mystic over a

99\%

chance to make an accurate prediction.

Problem Statement