ABSTRACT
This chapter explores the power of probabilistic thinking, even, on occasion, for problems that don't appear to have anything to do with chance. Twenty-six puzzles and a theorem demonstrate the technique; along the way, the basic rules of probability are reviewed, including Bayes' formula for conditional probabilities. The puzzles concern winning at tennis, finding a birthday match, shooting at a target, playing in sports tournaments, testing coins, and even deciding what type of court-martial to hope for. Several of the puzzles yield to a technique called “coupling” in which probabilities are compared by imagining situations in which the associated events compete directly. Finally, the theorem computes the probability that a candidate who won an election led all the way.
