Ron Larson
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8.3 Expected Value

8.3 Expected Value
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  • 11. Comparing Options

    Compare the two options. (See Example 5.)

    • Worked-Out Solution

      According to expected value, the second option would pay better in the long run. Which would you choose? Would you choose a 100% chance of getting $1000 or a 60% chance of getting $2000?

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      ______     ___     _____       ___      ______  
 /_____//   / _ \\  |  __ \\    / _ \\   /_   _// 
 `____ `   | / \ || | |  \ ||  | / \ ||    | ||   
 /___//    | \_/ || | |__/ ||  | \_/ ||   _| ||   
 `__ `      \___//  |_____//    \___//   /__//    
 /_//       `---`    -----`     `---`    `--`     
 `-`
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  • 12. Comparing Options

    Compare the two options. (See Example 5.)

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      ______    ______             _    _     ______  
 /_   _//  /_   _//     ___   | || | ||  /_   _// 
   | ||     -| ||-     /   || | || | ||  `-| |,-  
  _| ||     _| ||_    | [] || | \\_/ ||    | ||   
 /__//     /_____//    \__ ||  \____//     |_||   
 `--`      `-----`      -|_||   `---`      `-`'   
                         `-`
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  • 13. Comparing Options

    Compare the two options. (See Example 5.)

    • Worked-Out Solution

      According to expected value, the second option would pay better in the long run. Remember, however, that 10% of the time, the second option results in $0.

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     _    _    __   __   __   _    _    _    _____    
| \  / ||  \ \\/ // | || | || | || | || |  __ \\  
|  \/  ||   \ ` //  | '--' || | || | || | |  \ || 
| .  . ||    | ||   | .--. || | \\_/ || | |__/ || 
|_|\/|_||    |_||   |_|| |_||  \____//  |_____//  
`-`  `-`     `-`'   `-`  `-`    `---`    -----`
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  • 14. Comparing Options

    Compare the two options. (See Example 5.)

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                _____     ______     ___      ____    
  ____     |  ___||  /_   _//   / _ \\   |  _ \\  
 |    \\   | ||__      | ||    / //\ \\  | |_| || 
 | [] ||   | ||__     _| ||   |  ___  || | .  //  
 |  __//   |_____||  /__//    |_||  |_|| |_|\_\\  
 |_|`-`    `-----`   `--`     `-`   `-`  `-` --`  
 `-`
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  • 15. Investment Comparison

    You want to invest $1000. Find the expected values for the two investments. (See Example 6.)

    • Worked-Out Solution

      A spreadsheet helps to organize the calculations.

        Speculative Investment

        Conservative Investment

      The speculative investment has a much greater expected value. By choosing this investment, however, you also have a better chance of losing everything.

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     _    _      ___     __   __     ___      ____    
| |  | ||   / _ \\   \ \\/ //   / _ \\   |  _ \\  
| |/\| ||  | / \ ||   \   //   / //\ \\  | |_| || 
|  /\  ||  | \_/ ||   / . \\  |  ___  || | .  //  
|_// \_||   \___//   /_//\_\\ |_||  |_|| |_|\_\\  
`-`   `-`   `---`    `-`  --` `-`   `-`  `-` --`
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  • 16. Investment Comparison

    You want to invest $1000. Find the expected values for the two investments. (See Example 6.)

    Comments (0)

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