Ron Larson
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8.4 Expecting the Unexpected

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

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

    Comments (0)

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

    Comments (0)

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