Clarifying the Language of Chance Using Basic Conditional Probability Reasoning: The Monty Hall Problem

The Monty Hall Problem

A range of solutions to the Monty Hall problem is developed, with the aim of connecting popular (informal) solutions and the formal mathematical solutions of introductory text-books. Under Riemann’s slogan of replacing calculations with ideas, we discover bridges between popular solutions and rigorous (formal) mathematical solutions by using various combinations of symmetry, symmetrization, ind...

The Monty Hall Problem is not a Probability

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch

Probability, rational single-case decisions and the Monty Hall Problem

The application of probabilistic arguments to rational decisions in a single case is a contentious philosophical issue which arises in various contexts. Some authors (e.g. Horgan, Philos Pap 24:209–222, 1995; Levy, Synthese 158:139–151, 2007) affirm the normative force of probabilistic arguments in single cases while others (Baumann, Am Philos Q 42:71–79, 2005; Synthese 162:265–273, 2008) deny ...

The Monty Hall Problem, Reconsidered

Probability, Rational Single-Case Decisions and the Monty Hall Problem

The application of probabilistic arguments to rational decisions in a single case is a contentious philosophical issue which arises in various contexts. Some authors (e.g. Horgan 1995; Levy 2007) affirm the normative force of probabilistic arguments in single cases while others (Baumann 2005, 2008) deny it. I demonstrate that both sides do not give convincing arguments for their case and propos...