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.)

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      ____       ___      ____     _    _             
 |  _ \\    / _ \\   |  _ \\  | || | ||     ___   
 | |_| ||  / //\ \\  | |_| || | || | ||    /   || 
 | .  //  |  ___  || | .  //  | \\_/ ||   | [] || 
 |_|\_\\  |_||  |_|| |_|\_\\   \____//     \__ || 
 `-` --`  `-`   `-`  `-` --`    `---`       -|_|| 
                                             `-`
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