Statistical Reasoning for Everyday Life (5th Edition)
5th Edition
ISBN: 9780134494043
Author: Jeff Bennett, William L. Briggs, Mario F. Triola
Publisher: PEARSON
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Textbook Question
Chapter 6.3, Problem 22E
Behind in Coin Tossing: Can You Catch Up? Suppose that you toss a fair coin 100 times, getting 38 heads and 62 tails, which is 24 more tails than heads.
- a. Explain why, on your next toss, the difference in the numbers of heads and tails is as likely to grow to 25 as it is to shrink to 23.
- b. Extend your explanation from part (a) to explain why, if you toss the coin 1000 more times, the final difference in the numbers of heads and tails is as likely to be larger than 24 as it is to be smaller than 24.
- c. Suppose that you continue tossing the coin. Explain why the following statement is true: If you stop at any random time, you always are more likely to have fewer heads than tails, in total.
- d. Suppose that you are betting on heads with each coin toss. After the first 100 tosses, you are well on the losing side (having lost the bet 62 times while winning only 38 times). Explain why, if you continue to bet, you will most likely remain on the losing side. How is this answer related to the gambler’s fallacy?
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Statistical Reasoning for Everyday Life (5th Edition)
Ch. 6.1 - Coin Tossing. Suppose you toss a coin 100 times....Ch. 6.1 - Statistical Significance. What do we mean when we...Ch. 6.1 - Prob. 3ECh. 6.1 - Quantifying Significance. What does it mean to say...Ch. 6.1 - Does It Make Sense? For Exercises 58, determine...Ch. 6.1 - Does It Make Sense? For Exercises 58, determine...Ch. 6.1 - Does It Make Sense? For Exercises 58, determine...Ch. 6.1 - Does It Make Sense? For Exercises 58, determine...Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Subjective Significance. For each event in...
Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Subjective Significance. For each event in...Ch. 6.1 - Prob. 17ECh. 6.1 - Carpal Tunnel Syndrome Treatments. An experiment...Ch. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Human Body Temperature. In a study by researchers...Ch. 6.1 - Seat Belts and Children. In a study of children...Ch. 6.1 - Prob. 23ECh. 6.1 - Subjective Significance. For each event in...Ch. 6.2 - Outcomes and Events. Distinguish between an...Ch. 6.2 - Notation. What does it mean when we write P(A)?...Ch. 6.2 - Probability Types. Briefly describe the...Ch. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Does It Make Sense? For Exercises 58, determine...Ch. 6.2 - Prob. 7ECh. 6.2 - Does It Make Sense? For Exercises 58, determine...Ch. 6.2 - Counting Outcomes. How many different three-child...Ch. 6.2 - Prob. 10ECh. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 1120, use...Ch. 6.2 - Days of the Week. What is the probability of...Ch. 6.2 - Days of the Week. What is the probability of...Ch. 6.2 - Complementary Events. Exercises 2330 involve...Ch. 6.2 - Complementary Events. Exercises 2330 involve...Ch. 6.2 - Complementary Events. Exercises 2330 involve...Ch. 6.2 - Complementary Events. Exercises 2330 involve...Ch. 6.2 - Complementary Events. Exercises 2330 involve...Ch. 6.2 - Complementary Events. Exercises 2330 involve...Ch. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Theoretical Probabilities. For Exercises 3134, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 3134, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 3134, use...Ch. 6.2 - Theoretical Probabilities. For Exercises 3134, use...Ch. 6.2 - Relative Frequency Probabilities. Use the relative...Ch. 6.2 - Relative Frequency Probabilities. Use the relative...Ch. 6.2 - Relative Frequency Probabilities. Use the relative...Ch. 6.2 - Prob. 38ECh. 6.2 - Probability Distributions. In Exercises 39 and 40,...Ch. 6.2 - Probability Distributions. In Exercises 39 and 40,...Ch. 6.3 - Law of Large Numbers. What is the law of large...Ch. 6.3 - Understanding the Law of Large Numbers. In terms...Ch. 6.3 - Expected Value. What is an expected value, and how...Ch. 6.3 - Gamblers Fallacy. What is the gamblers fallacy?...Ch. 6.3 - Prob. 5ECh. 6.3 - Does It Make Sense? For Exercises 58, determine...Ch. 6.3 - Prob. 7ECh. 6.3 - Does It Make Sense? For Exercises 58, determine...Ch. 6.3 - Gender Selection. In analyzing genders of...Ch. 6.3 - Speedy Driver. A person who has a habit of driving...Ch. 6.3 - Should You Play? Suppose you are offered this...Ch. 6.3 - Kentuckys Pick 4 Lottery. If you bet 1 in...Ch. 6.3 - Expected Value for Life Insurance. There is a...Ch. 6.3 - Expected Value for Life Insurance There is a...Ch. 6.3 - Expected Waiting Time. You arrive at a bus stop...Ch. 6.3 - Expected Value in Roulette. As shown in Figure...Ch. 6.3 - Expected Value in Casino Dice. When you give a...Ch. 6.3 - New Jersey Pick 4. In New Jerseys Pick 4 lottery,...Ch. 6.3 - Extra Points in Football. Football teams have the...Ch. 6.3 - Prob. 20ECh. 6.3 - Psychology of Expected Values. In 1953, a French...Ch. 6.3 - Behind in Coin Tossing: Can You Catch Up? Suppose...Ch. 6.4 - Risk and Travel. What is travel risk? Give an...Ch. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Does It Make Sense? For Exercises 58, determine...Ch. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Commercial Aviation. For Exercises 912, use the...Ch. 6.4 - Commercial Aviation. For Exercises 912, use the...Ch. 6.4 - Prob. 12ECh. 6.4 - Births/Deaths. For Exercises 1316, use the data in...Ch. 6.4 - Births/Deaths. For Exercises 1316, use the data in...Ch. 6.4 - Births/Deaths. For Exercises 1316, use the data in...Ch. 6.4 - Births/Deaths. For Exercises 1316, use the data in...Ch. 6.4 - Vital Statistics. For Exercises 1720, use the data...Ch. 6.4 - Vital Statistics. For Exercises 1720, use the data...Ch. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - Prob. 21ECh. 6.4 - Prob. 22ECh. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Prob. 28ECh. 6.4 - Life in This Century. Example 5 assumed that the...Ch. 6.4 - Prob. 30ECh. 6.5 - Independence. Let A denote the event of getting a...Ch. 6.5 - Independence. A geneticist is working with 3 green...Ch. 6.5 - Prob. 3ECh. 6.5 - Complementary Events. Let A be the event of...Ch. 6.5 - Prob. 5ECh. 6.5 - Does It Make Sense? For Exercises 58, determine...Ch. 6.5 - Does It Make Sense? For Exercises 58, determine...Ch. 6.5 - Does It Make Sense? For Exercises 58, determine...Ch. 6.5 - Births. Assume that boys and girls are equally...Ch. 6.5 - Births. A couple plans to have four children. Find...Ch. 6.5 - Password. A programmer is instructed to create a...Ch. 6.5 - Wearing Hunter Orange. A study of hunting injuries...Ch. 6.5 - Songs. The 50 songs on a smartphone consist of 15...Ch. 6.5 - Polls. A pollster plans to call adults. She has a...Ch. 6.5 - Probability and Court Decisions. In Exercises...Ch. 6.5 - Probability and Court Decisions. In Exercises...Ch. 6.5 - Probability and Court Decisions. In Exercises...Ch. 6.5 - Probability and Court Decisions. In Exercises...Ch. 6.5 - Probability and Court Decisions. In Exercises...Ch. 6.5 - Probability and Court Decisions. In Exercises...Ch. 6.5 - Prob. 21ECh. 6.5 - Pedestrian Deaths. For Exercises 2126, use the...Ch. 6.5 - Prob. 23ECh. 6.5 - Pedestrian Deaths. For Exercises 2126, use the...Ch. 6.5 - Prob. 25ECh. 6.5 - Pedestrian Deaths. For Exercises 2126, use the...Ch. 6.5 - Clinical Trial. In a clinical trial of an allergy...Ch. 6.5 - Prob. 28ECh. 6.5 - Prob. 29ECh. 6.5 - Survey Refusals. Refer to the data in Exercise 29....Ch. 6.5 - Drug Testing. A 1-Panel-THC test for marijuana use...Ch. 6.5 - BINGO. The game of BINGO involves drawing numbered...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - For Exercises 17, use the data in the following...Ch. 6 - The Binary Computer Company manufactures computer...Ch. 6 - For a recent year, the fatality rate from motor...Ch. 6 - A Las Vegas handicapper can correctly predict the...Ch. 6 - For the handicapper in Exercise 1, find the...Ch. 6 - In a clinical trial of the effectiveness of a...Ch. 6 - If P(A) = 0.65, what is the value of P(not A)?Ch. 6 - In Exercises 610, use the following results. The...Ch. 6 - In Exercises 610, use the following results. The...Ch. 6 - Prob. 8CQCh. 6 - In Exercises 610, use the following results. The...Ch. 6 - In Exercises 610, use the following results. The...
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