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8.2 Estimating Likelihood

8.2 Estimating Likelihood
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  • 9. Finding an Experimental Probability

    The tables show the results of a survey that asked whether the Internet is a main news source. Find the probability that a person in the 18-29 age group says "yes." (See Example 3 and Example 4.)

    • Worked-Out Solution

      In the 18-29 age group, there are 259 + 141 = 400 people. Of these, 259 responded with "yes" in the survey. So, based on this sample, the probability that a randomly chosen person in this age group would say "yes" is

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     _    _     ______   __   _      ___      _____   
    | \  / ||  /_   _// | || | ||   / _ \\   |__  //  
    |  \/  ||   -| ||-  | '--' ||  / //\ \\    / //   
    | .  . ||   _| ||_  | .--. || |  ___  ||  / //__  
    |_|\/|_||  /_____// |_|| |_|| |_||  |_|| /_____|| 
    `-`  `-`   `-----`  `-`  `-`  `-`   `-`  `-----`  
                                                      
    
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  • 10. Finding an Experimental Probability

    The tables show the results of a survey that asked whether the Internet is a main news source. Find the probability that a person in the 65 and over age group says "yes." (See Example 3 and Example 4.)

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     _____     __   __   ______      ___      ______  
    |  __ \\   \ \\/ // |      \\   / _ \\   /_   _// 
    | |  \ ||   \ ` //  |  --  //  | / \ ||  `-| |,-  
    | |__/ ||    | ||   |  --  \\  | \_/ ||    | ||   
    |_____//     |_||   |______//   \___//     |_||   
     -----`      `-`'   `------`    `---`      `-`'   
                                                      
    
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  • 11. Finding an Experimental Probability

    The tables show the results of a survey that asked whether the Internet is a main news source. Find the probability that a person in any age group says "no." (See Example 3 and Example 4.)

    • Worked-Out Solution

      Using the age group table, add the data in the "Yes" and "No" columns.

      Based on this sample, the probability that a randomly chosen person would say "no" is

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      _____      ___      ______    ______   _    _   
     / ____||   / _ \\   /_____//  /_   _// | || | || 
    / //---`'  | / \ ||  `____ `    -| ||-  | || | || 
    \ \\___    | \_/ ||  /___//     _| ||_  | \\_/ || 
     \_____||   \___//   `__ `     /_____//  \____//  
      `----`    `---`    /_//      `-----`    `---`   
                         `-`                          
    
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  • 12. Finding an Experimental Probability

    The tables show the results of a survey that asked whether the Internet is a main news source. Find the probability that a person in any region says "no." (See Example 3 and Example 4.)

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      _  _    _    _     ______    _____     _  _   
     | \| || | || | ||  /_   _//  |  ___||  | \| || 
     |  ' || | || | ||  `-| |,-   | ||__    |  ' || 
     | .  || | \\_/ ||    | ||    | ||__    | .  || 
     |_|\_||  \____//     |_||    |_____||  |_|\_|| 
     `-` -`    `---`      `-`'    `-----`   `-` -`  
                                                    
    
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  • 13. Data Analysis

    The tables show the results of a survey that asked whether the Internet is a main news source. Compare your answers to Exercises 11 and 12. What do you notice?

    • Worked-Out Solution

      Age Groups: Using the age group table, add the data in the "Yes" and "No" columns.

      Based on this sample, the probability that a randomly chosen person would say "no" is

      Regions: Using the region table, add the data in the "Yes" and "No" columns.

      Based on this sample, the probability that a randomly chosen person would say "no" is

      So, you obain the same answer regardless of which table you use.

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      ______   __   __   __   __     ___              
     /_   _//  \ \\/ //  \ \\/ //   / _ \\      ___   
       | ||     \ ` //    \   //   / //\ \\    /   || 
      _| ||      | ||     / . \\  |  ___  ||  | [] || 
     /__//       |_||    /_//\_\\ |_||  |_||   \__ || 
     `--`        `-`'    `-`  --` `-`   `-`     -|_|| 
                                                 `-`  
    
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  • 14. New Year's Resolutions

    The graphs show the results of a survey that asked men and women in different body mass index (BMI) categories whether losing weight is one of their New Year's resolutions.

    Find the probability that losing weight is one of the New Year's resolutions for each gender. Then describe the likelihood. (See Example 3 and Example 4.)

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      _  _    _    _     _  __   _    _     ______  
     | \| || | || | ||  | |/ // | || | ||  /_   _// 
     |  ' || | || | ||  | ' //  | || | ||  `-| |,-  
     | .  || | \\_/ ||  | . \\  | \\_/ ||    | ||   
     |_|\_||  \____//   |_|\_\\  \____//     |_||   
     `-` -`    `---`    `-` --`   `---`      `-`'   
                                                    
    
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  • 15. New Year's Resolutions

    The graphs show the results of a survey that asked men and women in different body mass index (BMI) categories whether losing weight is one of their New Year's resolutions.

    Find the probability that losing weight is one of the New Year's resolutions for a person in each BMI category. Then describe the likelihood. (See Example 3 and Example 4.)

    • Worked-Out Solution

      Underweight: There are 25 + 143 = 168 underweight people in the survey. Of these, 25 said that losing weight is one of their New Year's resolutions. So, based on this survey, the probability that an underweight person chosen at random will say that losing weight is one of his or her New Year's resolutions is

      Normal weight: There are 140 + 462 = 602 normal weight people in the survey. Of these, 140 said that losing weight is one of their New Year's resolutions. So, based on this survey, the probability that a normal weight person chosen at random will say that losing weight is one of his or her New Year's resolutions is

      Overweight: There are 491 + 511 = 1002 overweight people in the survey. Of these, 491 said that losing weight is one of their New Year's resolutions. So, based on this survey, the probability that an overweight person chosen at random will say that losing weight is one of his or her New Year's resolutions is

      Obese: There are 352 + 244 = 596 obese people in the survey. Of these, 352 said that losing weight is one of their New Year's resolutions. So, based on this survey, the probability that an obese person chosen at random will say that losing weight is one of his or her New Year's resolutions is

      Morbidly obese: There are 123 + 75 = 198 morbidly obese people in the survey. Of these, 123 said that losing weight is one of their New Year's resolutions. So, based on this survey, the probability that a morbidly obese person chosen at random will say that losing weight is one of his or her New Year's resolutions is

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      _____     ______   __   __   _    _     ______  
     /  ___||  /_   _//  \ \\/ // | || | ||  /_   _// 
    | // __     -| ||-    \   //  | || | ||  `-| |,-  
    | \\_\ ||   _| ||_    / . \\  | \\_/ ||    | ||   
     \____//   /_____//  /_//\_\\  \____//     |_||   
      `---`    `-----`   `-`  --`   `---`      `-`'   
                                                      
    
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  • 16. Finding Trends

    The graphs show the results of a survey that asked men and women in different body mass index (BMI) categories whether losing weight is one of their New Year's resolutions.

    Describe any trends you see in the graphs. (See Example 3 and Example 4.)

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      _____      ___       _____   _    _    __   __  
     / ____||   / _ \\    / ___// | || | ||  \ \\/ // 
    / //---`'  | / \ ||   \___ \\ | || | ||   \   //  
    \ \\___    | \_/ ||   /    // | \\_/ ||   / . \\  
     \_____||   \___//   /____//   \____//   /_//\_\\ 
      `----`    `---`   `-----`     `---`    `-`  --` 
                                                      
    
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