## Arnab Chakraborty on The Monty Hall Problem and Bayes’ Theorem – The Central Equilibrium – Episode 6

I am pleased to welcome Arnab Chakraborty back to my talk show, “The Central Equilibrium“, to talk about the Monty Hall Problem and Bayes’ theorem.  In this episode, he shows 2 solutions to this classic puzzle in probability, and invokes Bayes’ Theorem for the second solution.

If you have not watched Arnab’s first episode on Bayes’ theorem, then I encourage you to do that first.

Marilyn Vos Savant provided a solution to this problem in PARADE Magazine in 1990-1991.  Thousands of readers disagreed with her solution and criticized her vehemently (and incorrectly) for her error.  Some of these critics were mathematicians!  She included some of those replies and provided alternative perspectives that led to the same conclusion.  Although I am dismayed by the disrespect that some people showed in their letters to her, I am glad that a magazine column on probability was able to attract so much readership and interest.  Arnab and I referred to one of her solutions in our episode.  Thank you, Marilyn!

Enjoy this episode of “The Central Equilibrium“!

## Arnab Chakraborty on Bayes’ Theorem – The Central Equilibrium – Episode 3

Arnab Chakraborty kindly came to my new talk show, “The Central Equilibrium”, to talk about Bayes’ theorem.  He introduced the concept of conditional probability, stated Bayes’ theorem in its simple and general forms, and showed an example of how to use it in a calculation.

Check it out!

## Detecting Unfair Dice in Casinos with Bayes’ Theorem

#### Introduction

I saw an interesting problem that requires Bayes’ Theorem and some simple R programming while reading a bioinformatics textbook.  I will discuss the math behind solving this problem in detail, and I will illustrate some very useful plotting functions to generate a plot from R that visualizes the solution effectively.

#### The Problem

The following question is a slightly modified version of Exercise #1.2 on Page 8 in “Biological Sequence Analysis” by Durbin, Eddy, Krogh and Mitchison.

An occasionally dishonest casino uses 2 types of dice.  Of its dice, 97% are fair but 3% are unfair, and a “five” comes up 35% of the time for these unfair dice.  If you pick a die randomly and roll it, how many “fives”  in a row would you need to see before it was most likely that you had picked an unfair die?”

Read more to learn how to create the following plot and how it invokes Bayes’ Theorem to solve the above problem!