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A random, 7-digit positive integer is selected. What is the most likely value for the sum of its digits?

Bonus: Generalize your answer to \(n\)-digit integers.

A monkey is typing a string of random letters, with all letters equally (and independently) likely to be typed.

Which word is more likely to appear first in the string ...

Is it possible to fill a \(2017 \times 2017\) square grid with \(2017^2\) distinct positive integers such that the product of the numbers in each row and each column ...

On an \(n \times n\) square grid, two vertices are chosen at random and a segment is drawn connecting them. As \(n\rightarrow \infty,\) what is the probability that the ...

Forest fires are a fact of life on a planet covered in trees. Some are minor occurrences, burning over a few acres before being snuffed out without event, while others ...

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