## Detecting Unfair Dice in Casinos with Bayes’ Theorem

October 30, 2013 Leave a comment

#### 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!**

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