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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