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# APPLIED RESEARCH TOOLS MAN 6325

University of Central Florida

GPA 3.85

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This 8 page Class Notes was uploaded by Miss Kristopher Farrell on Thursday October 22, 2015. The Class Notes belongs to MAN 6325 at University of Central Florida taught by Stephen Goodman in Fall. Since its upload, it has received 54 views. For similar materials see /class/227677/man-6325-university-of-central-florida in Business, management at University of Central Florida.

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Date Created: 10/22/15

MN 6325 Spring 2009 PMSM Program Chapter 4 Probability Fundamentals Work wet Key Page 1 0f 8 RULE OF COMPLEMENTS WORKSHEET Assume you have a standard deck of cards bridge or poker deck with 52 cards You will draw a card at random from the deck Answer the questions below Question Question Answer 1 What is the probability that the randomly drawn card will be a red 2652 l2 card 5 2 What is the probability that the randomly drawn card will not be a 1 5 5 red card ie the probability that it will be a black card 39 39 3 What is the probability that the randomly drawn card will be a 1352 14 spade 25 4 What is the probability that the randomly drawn card will not be a 1 25 75 spade ie it will be either a heart club or diamond 39 39 MN 6325 Spring 2009 PMSM Program Chapter 4 Probability Fundamentals Work wet K ey Page 2 0f 8 RULE OF ADDITION WORKSHEET Assume you have a standard deck of cards bridge or poker deck with 52 cards You will draw a card at random from the deck Answer the questions below Question set A Question Question Answer 1 What is the probability that the randomly drawn card will be a king or a queen PK 452 PQ 452 7 7 1538 2 What is the probability that the randomly drawn card will be a heart 13 5213 52 or a spade PH1352 PS1352 12 5 Mutually exclusive PA PB Question set B Question Question Answer What is the probability that the randomly drawn card will be a spade 1652 1 or an ace PS 1352 PA 452 PS and A 152 413 1352 452 152 1652 3077 What is the probability that the randomly drawn card will be a face 2252 2 card or a heart PF 1252 PH 1352 PF and H 352 1126 1252 1352 352 2252 4231 Not mutually exclusive PA PB PA and B MN 6325 Spring 2009 PMSM Program Chapter 4 Probability Fundamentals Work wet K ey Page 3 0f 8 CONDITIONAL PROBABILITY WORKSHEET Situations Where There Is Statistical Independence Assume you have a standard deck of cards bridge or poker deck with 52 cards You will draw a card at random from the deck Answer the questions below Question set C1 Question Question Answer 1 What is the probability that the randomly drawn card will be a 1352 14 spade 25 2 What is the probability that the randomly drawn card will be a 452 1 13 queen 0769 What is the probability that the randomly drawn card will be the 1 52 3 queen of spades 0192 Question set C2 Question Question Answer Suppose we know that the randomly drawn card is a spade 113 1 Knowing this what is the probability that the randomly drawn card 0769 is the queen of spades 1521352 39 Question set D1 Question Question Answer 1 What is the probability that the randomly drawn card will be a red 2652 12 card 5 2 What is the probability that the randomly drawn card will be a face 12 52 3 13 card 2308 3 What is the probability that the randomly drawn card will be a red 6 52 326 face card 1154 Question set D2 Question Question Answer Suppose we know that the randomly drawn card is a red card 313 1 Knowing this what is the probability that the randomly drawn card 2308 is a red face card6522652 313 39 MN 6325 Spring 2009 PMSM Program Chapter 4 Probability Fundamentals Work wet K ey Page 4 0f 8 CONDITIONAL PROBABILITY WORKSHEET Situations Where There Is Statistical Dependence Assume you have a standard deck of cards bridge or poker deck with 52 cards You will draw a card at random from the deck Answer the questions below Question set E1 Question Question Answer 1 What is the probability that the randomly drawn card will be a 1352 14 heart 25 2 What is the probability that the randomly drawn card will be red 6552 12 3 What is the probability that the randomly drawn card will be a heart 1352 25 and red Question set E2 Question Question Answer Suppose we know that the randomly drawn card is red Knowing 1 this what is the probability that the randomly drawn card is a heart 12 5 14 1 2 Question set F1 Question Question Answer What is the probability that the randomly drawn card will be an 2052 5 13 1 7 even numbered card 7 3846 What is the probability that the randomly drawn card will be a 40 5210 13 2 7 39 A card 7 7692 What is the probability that the randomly drawn card will be a 2052 513 3 I 1 7 and even card 7 3846 Question set F2 Question Question Answer Suppose we know that the randomly drawn card is a numbered card 1 Knowing this what is the probability that the randomly drawn card 5 is an even numbered card 20524052 2040 5 MN 6325 Spring 2009 PMSM Program Chapter 4 Probability Fundamentals WorkMeet Key Page 5 0f 8 S 39 39 Face Value amtSuit In C1 we were interested in the probability that a card is a queen and a spade Our intuition might tell us that face value is not related to suit but we can check that out to verify Rule of multiplication suggests PQ and S PQ given S X PS Since PQ given S 113 and PS 1352 PQ and S 113 X 1352 152 If face value and color are independent PQ and S should PQ X PS PQ X PS 452 X 1352 152 which is the same value returned from the rule of multiplication therefore it has been verified that face value and color are statistically independent Face Value and Color In D1 we were interested in the probability that a card is a face card and red Our intuition might tell us that face value is not related to color but we can check that out to verify Rule of multiplication suggests PF and R PF given R X PR Since PF given R 626 and PR 2652 PF and R 626 X 2652 652 If face value and color are independent PF and R should PF X PR PF X PR 1252 X 2652 652 which is the same value returned from the rule of multiplication therefore it has been verified that face value and color are statistically independent MN 6325 Spring 2009 PMSM Program Chapter 4 Probability Fundamentals WorkMeet Key Page 6 0f 8 quot 39 39 I Suit and Color In El we were interested in the probability that a card is a heart and red Our intuition should tell us that suit is related to color but we can check that out to verify Rule of multiplication suggests PH and R PH given R X PR Since PH given R 1326 and PR 2652 PH and R 1326 X 2652 1352 25 If suit and color are independent PH and R should PH X PR PH X PR 1352 X 2652 18 125 which is not the same value returned from the rule of multiplication therefore it has been veri ed that suit and color are statistically dependent quot 39 39 I OddEven andFaceNumber Status In F1 we were interested in the probability that a card is an even card and a numbered card Again our intuition should tell us that oddeven status is related to category face vs number but we can check that out to verify Rule of multiplication suggests PE and N PE given N X PN Since PE given N 2040 and PN 4052 PE and N 2040 X 4052 2052 3846 If odd even and facenumber are independent PE and N should PE X PN PE X PN 2052 X 4052 50169 2959 which is not the same value returned from the rule of multiplication therefore it has been verified that oddeven status and facenumber status are statistically dependent MN 6325 Spring 2009 PMSM Program Chapter 4 Probability Fundamentals Work wet Key Page 7 0f 8 ANOTHER STATISTICAL DEPENDENCE ILLUSTRATION We have to move away from the cards for the moment The table below shows information about a graduate course that was taught several times in the past total of 200 students responded to a questionnaire Each of the respondents received either a satisfactory grade denoted by S or an unsatisfactory grade denoted by U Student preparation for exams differed some students were diligent about thoroughly reading the notes I posted on the intemet denoted as R while others simply listened to me in class and did no further studying denoted as L The table below summarizes the findings Final Grade S U Total 0 R 90 10 100 33 L 60 40 100 Total 150 50 200 Question Question Answer 150200 1 What 1s the probab111ty that a student w1ll get a sat1sfactory grade 75 50200 2 What 1s the probab111ty that a student w1ll get an unsat1sfactory grade 25 3 What is the probability that a student will read the notes 1002500 4 What is the probability that a student will simply listen in class 1002500 The answers to questions l4 re ect the marginal probabilities probabilities on the margins of the table They are the probabilities of simple events Question Question Answer What is the probability that a student will read the notes and get a 90200 5 sat1sfactory grade 1n the course 45 6 What is the probability that a student will read the notes and get an 10200 quot f y grade in the course 05 7 What is the probability that a student will simply listen in class and 60200 get a quot f y grade in the course 30 8 What is the probability that a student will simply listen in class and 40200 get an quot f y grade in the course 20 The answers to questions 58 re ect the joint probabilities of two events occurring together MN 6325 Spring 2009 PMSM Program Chapter 4 Probability Fundamentals Work wet K ey Page 8 0f 8 Based on the historical data The probability that a student will get a satisfactory grade PS 150200 75 The probability that a student will get an unsatisfactory grade PU 50200 25 The probability that a student will read the notes PR 100200 5 The probability that a student will simply listen in class PL 100200 5 The probability that a student will read and get a satisfactory grade PR H S 90200 45 The probability that a student will read and get an unsatisfactory grade PR f U 10200 05 The probability that a student will listen and get a satisfactory grade PL f S 60200 3 The probability that a student will listen and get an unsatisfactory grade PL f S 40200 2 It can be further noted that The probability of satisfactory given read PS I R 90 100 9 The probability of unsatisfactory given read PU I R 10 100 l The probability of satisfactory given listen PS I L 60 100 6 The probability of unsatisfactory given listen PU I L 40 100 4 Check the 39 39 quotI 39 rule PS H R PS X PR ie PS and R PS X PR See ifthis is true PS and R PS x PR 755 375 45 above Check the 39 39 quotI rule PS H R PS I R X PR read as PS and R PS given R X PR 95 45 F inallv 39 would suggest that PS I R PS ie PS given R PS See ifthis is true PS R 9 PS 75 They are not equal so they are not independent

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