Ron Larson
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8.1 Assigning a Measure to Likelihood

8.1 Assigning a Measure to Likelihood
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  • 7. Fatal Occupational Injuries

    The graph shows the rates of fatal occupational injuries per 100,000 full-time workers for several industries. (See Example 3.)

    1. Compare the rates of fatal occupational injuries for the different industries.
    2. Why do different industries have different rates?

    • Worked-Out Solution
      1. Even in the most dangerous of the industries, the annual rate of fatal injury is

        which means that a fatal industrial accident is very unlikely. Of the industries shown in the graph, mining is the most dangerous.

      2. Industries differ in fatality rates for the obvious reason that some industries are much more dangerous than others. The Occupational Safety & Health Administration (OSHA) posts data at its website on fatalities in various industries.
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     _    _    _    _     _  __    ______    _  _   
| \  / || | || | ||  | |/ //  /_   _//  | \| || 
|  \/  || | || | ||  | ' //    -| ||-   |  ' || 
| .  . || | \\_/ ||  | . \\    _| ||_   | .  || 
|_|\/|_||  \____//   |_|\_\\  /_____//  |_|\_|| 
`-`  `-`    `---`    `-` --`  `-----`   `-` -`
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  • 8. Fatal Occupational Injuries

    The graph shows the numbers of fatal occupational injuries for the same industries as in Exercise 7. (See Example 3.)

    1. Compare the numbers of fatal occupational injuries for the different industries.
    2. Explain why financial activities and mining have the same number of fatal occupational injuries, but their rates in Exercise 7 are different.

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    __    __   _    _      _____   _    _     _____   
\ \\ / // | || | ||   / ___// | || | ||  |__  //  
 \ \/ //  | || | ||   \___ \\ | || | ||    / //   
  \  //   | \\_/ ||   /    // | \\_/ ||   / //__  
   \//     \____//   /____//   \____//   /_____|| 
    `       `---`   `-----`     `---`    `-----`
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  • 9. Nuclear Plant Meltdown

    Determine the likelihood and significance of a nuclear plant meltdown. (See Example 4.)

    • Worked-Out Solution

      A meltdown at a nuclear plant, like that at Fukushima pictured below, is extremely unlikely but highly significant.

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      _____      ___     __   __   __   __    _____   
 |__  //    / _ \\   \ \\/ //  \ \\/ //  / ____|| 
   / //    / //\ \\   \   //    \ ` //  / //---`' 
  / //__  |  ___  ||  / . \\     | ||   \ \\___   
 /_____|| |_||  |_|| /_//\_\\    |_||    \_____|| 
 `-----`  `-`   `-`  `-`  --`    `-`'     `----`
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  • 10. Foodborne Illness

    Determine the likelihood and significance of contracting a foodborne illness during your lifetime. (See Example 4.)

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      ______     ___                 ___      _  _   
 /_   _//   / _ \\    ____      / _ \\   | \| || 
 `-| |,-   / //\ \\  |    \\   | / \ ||  |  ' || 
   | ||   |  ___  || | [] ||   | \_/ ||  | .  || 
   |_||   |_||  |_|| |  __//    \___//   |_|\_|| 
   `-`'   `-`   `-`  |_|`-`     `---`    `-` -`  
                     `-`
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  • 11. Flood Damage

    Determine the likelihood and significance of a flood damaging property on a hilltop. (See Example 4.)

    • Worked-Out Solution

      A flood damaging property on a hilltop like that pictured below in the Johnstown Flood of 1889, is extremely unlikely but highly significant.

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               _    _    ______      ___     _    _   
  ____    | || | || |      \\   / _ \\  | |  | || 
 |    \\  | || | || |  --  //  | / \ || | |/\| || 
 | [] ||  | \\_/ || |  --  \\  | \_/ || |  /\  || 
 |  __//   \____//  |______//   \___//  |_// \_|| 
 |_|`-`     `---`   `------`    `---`   `-`   `-` 
 `-`
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  • 12. Heart Disease

    Determine the likelihood and significance of a person with high blood pressure contracting heart disease. (See Example 4.)

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                 ___                 ___      _____   
  ____      / _ \\      ___     / _ \\   /  ___|| 
 |    \\   / //\ \\    /   ||  / //\ \\ | // __   
 | [] ||  |  ___  ||  | [] || |  ___  ||| \\_\ || 
 |  __//  |_||  |_||   \__ || |_||  |_|| \____//  
 |_|`-`   `-`   `-`     -|_|| `-`   `-`   `---`   
 `-`                     `-`
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  • 13. Deployed Air Bag

    Determine the likelihood and significance of a deployed air bag causing a severe injury. (See Example 4.)

    • Worked-Out Solution

      It is very unlikely that a deployed air bag will cause a severe injury. When this happens, however, it is significant.

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

    Determine the likelihood and significance of a heavy smoker contracting cancer. (See Example 4.)

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