### 8.4 Expecting the Unexpected

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• 1. Computer-Generated Sequence

A computer randomly generates a sequence of symbols. The circle graph shows the probability that the computer generates each of the symbols.

Find the probability that the sequence occurs. (See Example 1 and Example 2.)

• Worked-Out Solution

The probability that a given symbol is a cherry is 12%. So, the probability that all three symbols are cherries is

In other words, if the computer generated three symbols 100,000 times, you would expect 3 cherries to appear around 173 times.

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

```
• 2. Computer-Generated Sequence

A computer randomly generates a sequence of symbols. The circle graph shows the probability that the computer generates each of the symbols.

Find the probability that the sequence occurs. (See Example 1 and Example 2.)

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

```
• 3. Computer-Generated Sequence

A computer randomly generates a sequence of symbols. The circle graph shows the probability that the computer generates each of the symbols.

Find the probability that the sequence occurs. (See Example 1 and Example 2.)

• Worked-Out Solution

The probability that a given symbol is a watermelon is 8%. So, the probability that all three symbols are watermelons is

In other words, if the computer generated three symbols 100,000 times, you would expect 3 watermelons to appear around 51 times.

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

```
• 4. Computer-Generated Sequence

A computer randomly generates a sequence of symbols. The circle graph shows the probability that the computer generates each of the symbols.

Find the probability that the sequence occurs. (See Example 1 and Example 2.)

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

```
• 5. Computer-Generated Sequence

A computer randomly generates a sequence of symbols. The circle graph shows the probability that the computer generates each of the symbols.

Find the probability that the sequence occurs. (See Example 1 and Example 2.)

• Worked-Out Solution

The probability that a given symbol is a plum is 6%. So, the probability that all three symbols are plums is

In other words, if the computer generated three symbols 100,000 times, you would expect 3 plums to appear around 22 times.

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. Computer-Generated Sequence

A computer randomly generates a sequence of symbols. The circle graph shows the probability that the computer generates each of the symbols.

Find the probability that the sequence occurs. (See Example 1 and Example 2.)

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

```
• 7. Computer-Generated Sequence

A computer randomly generates a sequence of symbols. The circle graph shows the probability that the computer generates each of the symbols.

Find the probability that the sequence occurs. (See Example 1 and Example 2.)

• Worked-Out Solution

The probability that a given symbol is a seven is 2%. So, the probability that all three symbols are sevens is

In other words, if the computer generated three symbols 100,000 times, you would expect 3 sevens to appear only once.

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```  ______     ___                ______   ______
/_   _//   / _ \\    ____     /_   _// |      \\
| ||    | / \ ||  |    \\    -| ||-  |  --  //
_| ||    | \_/ ||  | [] ||    _| ||_  |  --  \\
/__//      \___//   |  __//   /_____// |______//
`--`       `---`    |_|`-`    `-----`  `------`
`-`
```
• 8. Slot Machine

Complete the spreadsheet to find the expected value of each of the events in Exercises 1-7. Then find the probability that a given spin is a "no win." Suppose these symbols represent a slot machine game. What is the expected value? Explain your reasoning. (See Example 1 and Example 2.)

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```  _____      ___                ______    ______