Chapter 5 Probability Distributions and Data Modeling 173 Empirical probability distribution Event Expected value Experiment Exponential distribution Goodness of fit Independent events Intersection Joint probability Joint probability table Marginal probability Multiplication law of probability Mutually exclusive Normal distribution Outcome Poisson distribution Probability Probability density function Probability distribution Probability mass function Random number Random number seed Random variable Random variate Sample space Standard normal distribution Uniform distribution Union Problems and Exercises 1. Lauren drinks a variety of soft drinks. Over the past month, she has had 15 diet colas, 4 cans of lemon- ade, and 6 cans of root beer in no particular order or pattern. a. Given this history, what is the probability that her next drink will be a diet cola? Lemonade? Root a. What are the outcomes of this experiment for one respondent? b. What is the probability that one respondent will rank Red Bull first? c. What is the probability that two respondents will both rank Red Bull first? beer? 5. Refer to the card scenario described in Problem 2. a. Let A be the event total card value is odd." Find P(A) and P(A). b. What is the probability that the sum of the two cards will be more than 14? b. What definition of probability did you use to answer this question? 2. Consider the experiment of drawing two cards with- out replacement from a deck consisting of only the ace through 10 of a single suit (e.g., only hearts). a. Describe the outcomes of this experiment. List the elements of the sample space. b. Define the event A, to be the set of outcomes for which the sum of the values of the cards is i (with an ace = 1). List the outcomes associated with A, for i = 3 to 19. c. What is the probability of obtaining a sum of the two cards equaling from 3 to 19? 3. Three coins are dropped on a table. a. List all possible outcomes in the sample space. b. Find the probability associated with each outcome. 4. A market research company surveyed consumers to determine their ranked preferences of energy drinks among the brands Monster, Red Bull, and Rockstar. 6. Refer to the coin scenario described in Problem 3. a. Let A be the event "exactly 2 heads." Find P(A). b. Let B be the event at most 1 head. Find P(B). c. Let C be the event at least 2 heads." Find P(C). d. Are the events A and B mutually exclusive? Find P(A or B). e. Are the events A and C mutually exclusive? Find P(A or C). 7. Roulette is played at a table similar to the one in Fig- ure 5.36. A wheel with the numbers 1 through 36 (evenly distributed with the colors red and black) and two green numbers 0 and 00 rotates in a shallow bowl with a curved wall. A small ball is spun on the inside of the wall and drops into a pocket corresponding to one of the numbers. Players may make 11 different types of bets by placing chips on different areas of Homework C Section A d. What is the probability at a shopper will not use any of these technologies? What is the probability that a shopper will check prices online and use online coupons but not use a smartphone? 1. Ifa slupper checks prices online, what is the protability that he or slie will use a sist ploone? 2. Wlal is the probability dial a slupper will check prices online bulbol use cline coupons or a smart plce? Go to Problems and Exercises on Page 173 of Chapter 5. Answer the following 5 questions as different tabs on excel file 25 points total, 5 naints each 24 17 Page 172 Page 174 Pare 1/1 Pace 175 Question and Question 5 Question 9 Question 12 Question 13 13 A Canadian basiness School summarized the gender and residency of its incoming class as follows: Residency Gerider Canada United States Eurove Asia Other 12.3 52 B Female 46 8 101 13 4 a. Construct the jout probability table. b. Calculate the margian probabilities c. What is the probability that a female student is fiom outside Canada or the United States Homework C-Section B-25 point total From a deck of cards, pull 20 cards. Aceis 1 and face cards are all 11. List them on excel. Now calculate descriptive statistics using excel and explain the results in your own words, 2 Consider the experiment af drawing two cars without replacement from a deck consisting of only the sce through 10 of n single suit (e 8., only hearts). Describe the outcomes of this cxpcricut. List the clemcuts of the sample space b. Detine the event to be the set of outcomes for which the sum of the values of the cards is (with an ace - 1). List ile outcomes associated will di luci - 3 lv 19. c. What is the probability of obtaining a sum of the two cards qualing from 3 to 192 5 Refer to the cant scenario described in Problem 2. Let A he the event "Total card value is add." Find Hand MA). b. What is the probability that the sum of the two cans will be more than 14? An airline tracks data on its flight arrivals. One the past 6 months, 50 flights on one toute stived early, 150 arrived on time, 25 were late, and 15 were caboclod. Whnt is the probability that in flight is early! On time! Iate? Canceled b. Are these outcomes mutually exclusive? 5. What is the probability that a flight is either early or on time! 12 A survey of shopping babits found the percentage of respondcuts that nec toclunology for shopping as shown in Figlue 5.37, Figure 5.37 Check Price Before Shopping 21.745 17.39% ca 17.305 Use One Coupons 435 Use aware towany Tur example, 17.39% only use online coupas: 21.74% se vcline coupons and check prices online before shopping, and so on. 2. Wat is die probability that a supper will check prices online before shopping? b What is the probability that shopper will use a smart phone to save money c. What is the probability that a shopper will use online coupeas? Chapter 5 Probability Distributions and Data Modeling 173 Empirical probability distribution Event Expected value Experiment Exponential distribution Goodness of fit Independent events Intersection Joint probability Joint probability table Marginal probability Multiplication law of probability Mutually exclusive Normal distribution Outcome Poisson distribution Probability Probability density function Probability distribution Probability mass function Random number Random number seed Random variable Random variate Sample space Standard normal distribution Uniform distribution Union Problems and Exercises 1. Lauren drinks a variety of soft drinks. Over the past month, she has had 15 diet colas, 4 cans of lemon- ade, and 6 cans of root beer in no particular order or pattern. a. Given this history, what is the probability that her next drink will be a diet cola? Lemonade? Root a. What are the outcomes of this experiment for one respondent? b. What is the probability that one respondent will rank Red Bull first? c. What is the probability that two respondents will both rank Red Bull first? beer? 5. Refer to the card scenario described in Problem 2. a. Let A be the event total card value is odd." Find P(A) and P(A). b. What is the probability that the sum of the two cards will be more than 14? b. What definition of probability did you use to answer this question? 2. Consider the experiment of drawing two cards with- out replacement from a deck consisting of only the ace through 10 of a single suit (e.g., only hearts). a. Describe the outcomes of this experiment. List the elements of the sample space. b. Define the event A, to be the set of outcomes for which the sum of the values of the cards is i (with an ace = 1). List the outcomes associated with A, for i = 3 to 19. c. What is the probability of obtaining a sum of the two cards equaling from 3 to 19? 3. Three coins are dropped on a table. a. List all possible outcomes in the sample space. b. Find the probability associated with each outcome. 4. A market research company surveyed consumers to determine their ranked preferences of energy drinks among the brands Monster, Red Bull, and Rockstar. 6. Refer to the coin scenario described in Problem 3. a. Let A be the event "exactly 2 heads." Find P(A). b. Let B be the event at most 1 head. Find P(B). c. Let C be the event at least 2 heads." Find P(C). d. Are the events A and B mutually exclusive? Find P(A or B). e. Are the events A and C mutually exclusive? Find P(A or C). 7. Roulette is played at a table similar to the one in Fig- ure 5.36. A wheel with the numbers 1 through 36 (evenly distributed with the colors red and black) and two green numbers 0 and 00 rotates in a shallow bowl with a curved wall. A small ball is spun on the inside of the wall and drops into a pocket corresponding to one of the numbers. Players may make 11 different types of bets by placing chips on different areas of Homework C Section A d. What is the probability at a shopper will not use any of these technologies? What is the probability that a shopper will check prices online and use online coupons but not use a smartphone? 1. Ifa slupper checks prices online, what is the protability that he or slie will use a sist ploone? 2. Wlal is the probability dial a slupper will check prices online bulbol use cline coupons or a smart plce? Go to Problems and Exercises on Page 173 of Chapter 5. Answer the following 5 questions as different tabs on excel file 25 points total, 5 naints each 24 17 Page 172 Page 174 Pare 1/1 Pace 175 Question and Question 5 Question 9 Question 12 Question 13 13 A Canadian basiness School summarized the gender and residency of its incoming class as follows: Residency Gerider Canada United States Eurove Asia Other 12.3 52 B Female 46 8 101 13 4 a. Construct the jout probability table. b. Calculate the margian probabilities c. What is the probability that a female student is fiom outside Canada or the United States Homework C-Section B-25 point total From a deck of cards, pull 20 cards. Aceis 1 and face cards are all 11. List them on excel. Now calculate descriptive statistics using excel and explain the results in your own words, 2 Consider the experiment af drawing two cars without replacement from a deck consisting of only the sce through 10 of n single suit (e 8., only hearts). Describe the outcomes of this cxpcricut. List the clemcuts of the sample space b. Detine the event to be the set of outcomes for which the sum of the values of the cards is (with an ace - 1). List ile outcomes associated will di luci - 3 lv 19. c. What is the probability of obtaining a sum of the two cards qualing from 3 to 192 5 Refer to the cant scenario described in Problem 2. Let A he the event "Total card value is add." Find Hand MA). b. What is the probability that the sum of the two cans will be more than 14? An airline tracks data on its flight arrivals. One the past 6 months, 50 flights on one toute stived early, 150 arrived on time, 25 were late, and 15 were caboclod. Whnt is the probability that in flight is early! On time! Iate? Canceled b. Are these outcomes mutually exclusive? 5. What is the probability that a flight is either early or on time! 12 A survey of shopping babits found the percentage of respondcuts that nec toclunology for shopping as shown in Figlue 5.37, Figure 5.37 Check Price Before Shopping 21.745 17.39% ca 17.305 Use One Coupons 435 Use aware towany Tur example, 17.39% only use online coupas: 21.74% se vcline coupons and check prices online before shopping, and so on. 2. Wat is die probability that a supper will check prices online before shopping? b What is the probability that shopper will use a smart phone to save money c. What is the probability that a shopper will use online coupeas