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8.3–8.4 Quiz

8.3–8.4 Quiz
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  • 1. Multiple-Choice Quiz

    You take a 10-question multiple-choice quiz. Each question has four choices. Suppose you guess when answering the questions. You gain 1 point when you answer a question correctly and 0 points when you answer a question incorrectly. What is the expected value of the quiz?

    • Worked-Out Solution

      For each question, you have a 25% probability of guessing the correct answer. So, your expected value for the 10 questions is

      In other words, if you consistently applied this test-taking strategy, over the long run, you should expect your test score average to be 2.5 points.

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      ______    ______   _____      ______   _    _   
     /_____//  /_   _// |  __ \\   /_   _// | || | || 
     `____ `    -| ||-  | |  \ ||   -| ||-  | || | || 
     /___//     _| ||_  | |__/ ||   _| ||_  | \\_/ || 
     `__ `     /_____// |_____//   /_____//  \____//  
     /_//      `-----`   -----`    `-----`    `---`   
     `-`                                              
    
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  • 2. Multiple-Choice Quiz

    You take a 10-question multiple-choice quiz. Each question has four choices. Suppose you guess when answering the questions. You gain 1 point when you answer a question correctly and lose ¼ point when you answer a question incorrectly. What is the expected value of the quiz?

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      _  _      ___      _  __   __   __    _____   
     | \| ||   / _ \\   | |/ //  \ \\/ //  |__  //  
     |  ' ||  / //\ \\  | ' //    \ ` //     / //   
     | .  || |  ___  || | . \\     | ||     / //__  
     |_|\_|| |_||  |_|| |_|\_\\    |_||    /_____|| 
     `-` -`  `-`   `-`  `-` --`    `-`'    `-----`  
                                                    
    
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  • 3. Multiple-Choice Quiz

    You take a 10-question multiple-choice quiz. Each question has four choices. Suppose you guess when answering the questions. What is the probability that you answer every question incorrectly?

    • Worked-Out Solution

      The probability that you answer every question incorrectly is

      So, with this test-taking strategy, you have about a 6% chance of answering every question incorrectly.

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       _____    _____    _    _      ___     __   __  
      / ___//  |  ___|| | || | ||   / _ \\   \ \\/ // 
      \___ \\  | ||__   | || | ||  | / \ ||   \   //  
      /    //  | ||__   | \\_/ ||  | \_/ ||   / . \\  
     /____//   |_____||  \____//    \___//   /_//\_\\ 
    `-----`    `-----`    `---`     `---`    `-`  --` 
                                                      
    
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  • 4. Multiple-Choice Quiz

    You take a 10-question multiple-choice quiz. Each question has four choices. Suppose you guess when answering the questions. What is the probability that you answer every question correctly?

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               _    _    _    _      ___     ______   
      ____    | || | || | \  / ||   / _ \\  |      \\ 
     |    \\  | || | || |  \/  ||  / //\ \\ |  --  // 
     | [] ||  | \\_/ || | .  . || |  ___  |||  --  \\ 
     |  __//   \____//  |_|\/|_|| |_||  |_|||______// 
     |_|`-`     `---`   `-`  `-`  `-`   `-` `------`  
     `-`                                              
    
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  • 5. Multiple-Choice Quiz

    You take a 10-question multiple-choice quiz. Each question has four choices. Suppose you guess when answering the questions. What is the probability that you answer only the first question correctly?

    • Worked-Out Solution

      The probability that you answer only the first question correctly is

      So, with this test-taking strategy, you have about a 2% chance of answering only the first question correctly.

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     _____      _____    __   _     ______    ______  
    |  __ \\   |  ___|| | || | ||  /_   _//  /_____// 
    | |  \ ||  | ||__   | '--' ||   -| ||-   `____ `  
    | |__/ ||  | ||__   | .--. ||   _| ||_   /___//   
    |_____//   |_____|| |_|| |_||  /_____//  `__ `    
     -----`    `-----`  `-`  `-`   `-----`   /_//     
                                             `-`      
    
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  • 6. Multiple-Choice Quiz

    You take a 10-question multiple-choice quiz. Each question has four choices. Suppose you guess when answering the questions. What is the probability that you answer only the first five questions correctly?

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      _  _      ___    __    __    _____     _  __  
     | \| ||   / _ \\  \ \\ / //  |  ___||  | |/ // 
     |  ' ||  | / \ ||  \ \/ //   | ||__    | ' //  
     | .  ||  | \_/ ||   \  //    | ||__    | . \\  
     |_|\_||   \___//     \//     |_____||  |_|\_\\ 
     `-` -`    `---`       `      `-----`   `-` --` 
                                                    
    
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  • 7. Multiple-Choice Quiz

    You take a 10-question multiple-choice quiz. Each question has four choices. Suppose you guess when answering the questions. What is the probability that you answer at least one question correctly?

    • Worked-Out Solution

      The probability that you answer every question incorrectly is

      So, the probability that you answer at least one quesiton correctly is

      So, with this test-taking strategy, you have about a 94% chance of answering at least one question correctly.

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