
Product No.
99771 
Supplementary Print 
Price:
FREE with membership 



The Probability that a Queen Sits Beside a King: Juxtapositions and Runs in a Random Permutation (UMAP)
John M. Holte, Mark M. Holte, and Kenneth A. Suman

Mathematics Topic: Probability, Statistics 
Application Areas: Statistics, applied probability, recreational mathematics 
Prerequisites: Combinatorics (addition/multiplication principles, permutations, combinations, and distributions of balls into urns); probability; statistics 

 ©1999 by COMAP, Inc.  Tools for Teaching 1998  22 pages 

This module deals with random permutations, focusing on probabilities, means, and variances of the numbers of juxtapositions and runs of items of different types. It illustrates the ideas via questions regarding a shuffled deck of standard playing cards, such as: What is the probability that a Queen is next to a King? What is the average number of juxtapositions? What is the variance? Tough problems are tamed. In a statistics course, this module provides a natural extension of the usual distribution theory of runs.
Table of Contents:
INTRODUCTION
THE PROBABILITY THAT A QUEEN IS NEXT TO A KING
JUXTAPOSITIONS AND RUNS
ORDERED JUXTAPOSITIONS
MEAN AND VARIANCE
RELATED PROBLEMS
RANDOM CIRCULAR PERMUTATIONS
SOLUTIONS
REFERENCES
ABOUT THE AUTHORS



