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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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