A Selection of Problems from A.A. Markov’s Calculus of Probabilities: Presenting the Problems

My translations of Markov's statements of the five selected problems are given on the following pages.

• Problem 1: Selecting balls from a vessel
• Problem 2: A lottery game
• Problem 3: Some generalizations of Problem 2
• Problem 4: A simple gambling game
• Problem 8: Sums of independent random variables

As a preface to each problem statement, I provide a few comments (in italics) at the top of the associated page. The original Russian statement of the problem is then given, followed by its English translation.

Links to my translation of Markov's solution for each problem are provided at the bottom of the associated statement page; my own commentaries on Markov's work appear either in footnotes or in italicized text on the solution pages.

Following my translation of the solution of Problem 8, I also provide my translation of Markov's analysis of the binomial distribution (as we would now call it) on the following three pages which should be read sequentially:

• Calculating probabilities of repeated independent events, Part 1
• Calculating probabilities of repeated independent events, Part 2
• Calculating probabilities of repeated independent events, Part 3