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

摘要

Clarity and preciseness in the use of language is crucial when communicating mathematical and probabilistic ideas. Lack of these can make even the simplest problem difficult to understand and solve. One such problem is the Monty Hall problem. In the past, a controversy was stirred among professional mathematicians when trying to reach a consensus on a solution to the problem. The problem still creates confusion among some of those who are asked to solve it for the first time. We purport to demonstrate the use of more precise language of basic conditional probability could have prevented the controversy.