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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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