ALTERNATIVE APPROACHES TO CONDITIONAL PROBABILITY USING MODELS OF GENETIC PEDIGREE, MONTY HALL PROBLEM & PRISONER’S PARADOX

ABSTRACT

The misapplication of conditional probability, the haphazard use of “equally likely” outcomes and the non use of Baye’s Rule can lead to all manner of incorrect answers. In this paper, we present and discuss three well-known examples of misapplication of the notion of conditional probability. In each example, we present the problem along with a published and/or well-known incorrect - but seemingly plausible - solution. We then give a careful treatment of the correct solution, in large part to show how careful application of basic probability rules can help students to spot and avoid these mistakes. With each example, we also hope to illustrate the importance & need for other display tools, specifically the tree diagram and sample space Venn diagram, when contingency tables do not readily apply i.e. for probability problems not involving data. 

FULL TEXT