### 8.3–8.4 Quiz

<
>
• 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.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

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

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

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

```
• 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.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

``` __   _      ___                ______    ______
| || | ||   / _ \\      ___    /_   _//  /_   _//
| '--' ||  | / \ ||    /   ||   -| ||-     | ||
| .--. ||  | \_/ ||   | [] ||   _| ||_    _| ||
|_|| |_||   \___//     \__ ||  /_____//  /__//
`-`  `-`    `---`       -|_||  `-----`   `--`
`-`
```
• 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?

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

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

```
• 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.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

``` _    _     _____               ______   __   _
| || | ||  |  ___||   ____     /_   _// | || | ||
| || | ||  | ||__    |    \\    -| ||-  | '--' ||
| \\_/ ||  | ||__    | [] ||    _| ||_  | .--. ||
\____//   |_____||  |  __//   /_____// |_|| |_||
`---`    `-----`   |_|`-`    `-----`  `-`  `-`
`-`
```
• 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?

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

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

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.
```  ______    ______    ______   __   __    ______