Combinatorics

This is the solution for problem 2 from Fifty Challenging Problems in Probability by Frederick Mosteller (1987). The problem is paraphrased below; for reference, it is inspired by the original book. Ellis is a tennis player who has to compete against two players: his father and the tennis club champion. The champion is a better player than the father. Ellis will play a three-set series with alternating opponents. He can either play his father first, then the champion, then his father again; or the champion first, then his father, then the champion again. If he wins two sets in a row, he wins a special prize. ...

This is the first post in a series solving problems from Fifty Challenging Problems in Probability by Frederick Mosteller (1987). The problem is paraphrased below; for reference, it is inspired by the original book. A drawer contains some red and black socks. Two socks are drawn at random, and the probability that both are red is \(1/2\). What is the minimum total number of socks? What is the minimum if the number of black socks is even? Let’s dive in! ...