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xxxii Review and practice for quizzes and tests Lesson 5.1 %u2022 Randomness, Probability, and%u00a0Simulation 335Building Concepts and Skills 1. The probability of any outcome of a chance process is a number between and . 2. Define the law of large numbers. 3. True/False: A common myth is that chance behavior is predictable in the short run. 4. List the three steps in performing a simulation. Mastering Concepts and Skills 5. Genetic testing It is not uncommon for both birth parents to carry the gene for cystic fibrosis without having the disease themselves. Suppose we select one of these parents at random. According to the laws of genetics, the probability that any child they have will develop cystic fibrosis is 0.25. If these birth parents have 4 children, is one child guaranteed to develop cystic fibrosis? Explain your If Arbor launches a favorite streaming radio channel at a randomly selected time, there is a 0.20 probability that a commercial If Arbor launches this channel at 5 randomly selected times, will there be exactly 1 time when a commercial is playing? Explain your answer. 7. Pedro drives the same route to work on Monday through Friday. The route includes one traffic light. According to the local traffic department, there is a 55% chance that the light will be red. Explain what this probability means. A local weather forecast says that there is a 20% chance of rain tomorrow. Explain what this probability means. 9. Jake is an insurance salesperson who is able to complete a sale in about 15% of calls Which of the following outcomes is more likely: HTHTTH or TTTHHH? Explain your answer. 12. No dice Imagine rolling a die 12 times and recording the result of each roll. Which of the following outcomes is more likely: 1 2 3 4 5 6 6 5 4 3 2 1 or 1 5 4 5 2 4 3 3 6 1 2 6? Explain your answer. 13. Streaky shootingthat a certain player is streaky. That is, the announcer believes that if the player makes a shot, the player is more likely to make the next shot. As evidence, the announcer points to a recent game where the player took 30 shots and had a streak of 10 made shots in a row. Is this convincing evidence of streaky shooting by the player? Assume that this player is a 50% shooter and that the results of each shot don%u2019t depend on previous shots. To help answer this question, we want to perform a simulation to estimate the probability that a 50% shooter who takes 30 shots would have a longest streak of 10 or more made shots.(a) Describe how to use a random number generator to perform one trial of the simulation. The dotplot displays the longest streak of made shots in each of 50 simulated games when this player took 30 shots. Longest streak in simulated game2 3 4 5 6 7 8 9 10(b) Explain what the dot at 10 represents. (c) Use the results of the simulation to estimate the probability that a 50% shooter who takes 30 shots would have a longest streak of 10 or more made shots. (d) Based on the actual result of 10 made shots in a row and your answer to part (c), is there convincpg 331 331pg 333 Exercises Lesson 5.1 W H AT D I D Y O U L E A R N ? LEARNING TARGET EXAMPLE EXERCISES Interpret probability as a long-run relative frequency. p. 331 5%u20138 Dispel common myths about randomness. p. 331 9%u201312 Use simulation to model chance behavior. p. 333 13%u201316 3. Describe how you would use a 10-sided die to perform one trial of this simulation. The dotplot shows the number of days on which the train arrived late in 100 trials of the simulation. 4. Explain what the dot at 7 represents. 5. Use the results of the simulation to estimate the probability that the train will arrive late on 3 or more of 20 days. 6. Based on the actual result of 3 late arrivals in 20%u00a0days and your answer to Question 5, is there convincing evidence that New Jersey Transit%u2019s claim%u00a0is false? Explain your reasoning. Simulated number of late arrivals0 1 2 3 4 5 6 706_StarnesSPA5e_53579_ch05_326_405.indd 334 22/11/24 1:45 PMof these parents at random. According to the laws of genetics, the probability that any child they have will develop cystic fibrosis is 0.25.(a) Interpret this probability. (b) If these birth parents have 4 children, is one child guaranteed to develop cystic fibrosis? Explain your answer. 6. Another commercial If Arbor launches a favorite streaming radio channel at a randomly selected time, there is a 0.20 probability that a commercial will be playing.(a) Interpret this probability. (b) If Arbor launches this channel at 5 randomly selected times, will there be exactly 1 time when a commercial is playing? Explain your answer. 7. Red light! Pedro drives the same route to work on Monday through Friday. The route includes one traffic light. According to the local traffic department, there is a 55% chance that the light will be red. Explain what this probability means. 8. Take the umbrella? A local weather forecast says that there is a 20% chance of rain tomorrow. Explain what this probability means. 9. Life insurance Jake is an insurance salesperson who is able to complete a sale in about 15% of calls pg 331 LOTS OF PROBLEMS FOR PRACTICE . Each lesson ends with about 25%u201330 exercises to assess mastery of the learning targets. %u2022 Building Concepts and Skills exercises focus on essential facts, definitions, and formulas from the lesson. %u2022 Mastering Concepts and Skills exercises are similar to the lesson%u2019s examples and typically feature two pairs of odd- and even-numbered exercises. %u2022 Applying the Concepts exercises combine several learning targets from the lesson in paired sets of odd- and even-numbered exercises. %u2022 Extending the Concepts exercises are more challenging problems that explore statistical concepts. %u2022 Recycle and Review exercises revisit content learned in previous lessons and set the stage for upcoming lessons. REVISIT THE CLEAR STRUCTURE. The %u201cWhat Did You Learn?%u201d grid shows which examples and exercises support each Learning Target. You can tell quickly how examples and exercises correspond. Imagine rolling a die 12 times and recording the result of each roll. Which of the following outcomes is more likely: 1 2 3 4 5 6 6 5 4 3 2 1 or 1 5 4 5 2 4 3 3 6 1 2 6? Explain your answer. Streaky shooting A basketball announcer suggests that a certain player is streaky. That is, the announcer believes that if the player makes a shot, the player is more likely to make the next shot. As evidence, the announcer points to a recent game where the player took 30 shots and had a streak of 10 made shots in a row. Is this convincing evidence of streaky shooting by the player? Assume that this player is a 50% shooter and that the results of each shot don%u2019t depend on previous shots. To help answer this question, we want to perform a simulation to estimate the probability that a 50% shooter who takes 30 shots would have a longest streak of 10 or more made shots. Describe how to use a random number generator to perform one trial of the simulation. The dotplot displays the longest streak of made shots in each of 50 simulated games when this player took 30 shots. THE %u201cBACKWARD/FORWARD%u201d NAVIGATION SYSTEM . Do you read the text first, or do you start with the assigned exercises? Either way, SPA is designed to support you. Look for the iconsthat appear next to selected exercises. They will guide you %u2022 Back to the example that models the exercise so that you can review the worked solution, if you are confused. %u2022 To a short video that provides step-by-step instruction for solving the exercise. Clicking the icons in the ebook lets you move back and forth quickly and easily. %u00a9 Bedford, Freeman & Worth Publishers. For review purposes only. Do not distribute.