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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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