LEADERSHIP PROGRAM IN DISCRETE MATHEMATICS CONTENT MAP FORM AUGUST 1994 A.1. TITLE OF DATABASE FILE: c9hGie.Markov A.2. TITLE OF ACTIVITY: The Markov Musician A.3. CATEGORY: Sequences and Dynamic Systems A.4. SUB-CATEGORY: Markov Chains A.5. PERSON CREATING FILE: Carol Giesing B.1. DESCRIPTION OF ACTIVITY: Paul, from Russian, practices classical guitar after school. He practices for 30 minutes or 60 minutes each day. If he practices for 30 minutes on a given day, it is equally likely he will practice 30 to 60 minutes the next day. However, only one out of five times will he play for 60 minutes 2 days in succession. Question: Given Monday Paul plays for 30 minutes. What is Probability he will play for 60 minutes on Wednesday? Picture of tree below. (Sort of) Mon Start .5 .5 60 Minutes 30 Minutes Day1/Mon .2 .8 .5 .5 60 Min 30 Min 60 Min 30 Min Day2/Tue .2 .8 .5 .5 .2 .8 .5 .5 60 Min 30 Min 60 Min 30 Min 60 Min 30 Min 60 Min 30 Min Day3/Wed Solution using the Tree is P(60 Min) = .25 + .10 = .35 NOTE: Matrix Mult. solution Entries in 1st row of product matrix are the probabilities for practicing 30 Minutes to 60 Minutes on Wed evening. Given 30Min 60Min 30Min 60Min 30Min | .5 .5 | | .5 .5 | = 30Min | .65 .35 | 60Min | .8 .2 | | .8 .2 | 60Min | .56 .44 | Answer is .35. B.2. RESOURCES USED FOR ACTIVITY: pencil and paper B.3. REFERENCE FOR ACTIVITY: Discrete Math Models by Fred Robert et al Discrete Math Across the Curriculum (NCTM Yearbook) Precalculus & Discrete Math C.1. GRADE LEVEL FOR ACTIVITY: high school C.3. STUDENT ABILITY LEVEL FOR ACTIVITY: middle to high C.3. LENGTH OF ACTIVITY: D.1. CONNECTIONS TO TRADITIONAL CURRICULUM: Probability D.2. CONNECTIONS TO OTHER SUBJECT AREAS: Algebra, Int. Alg, Precal D.3. PREREQUISITE DISCRETE MATH ACTIVITIES: Digraphs, Tree analysis D.4. SUBSEQUENT DISCRETE MATH ACTIVITIES THAT BUILD ON THIS ACTIVITY: