A storybook has 200 pages, numbered 1 to 200. Aarav lets the book fall open at a random page. What is the probability that the page number is a perfect cube?

The perfect cubes up to 200 are 1, 8, 27, 64 and 125 (the next one, 216, is past the last page) - five numbers. $P=\frac{5}{200}=\frac{1}{40}.\frac{3}{100}$ counts 216 as well; $\frac{7}{100}$ counts the 14 perfect SQUARES up to 200 instead; $\frac{1}{50}$ leaves out 1, which is $1\times 1\times 1$.