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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)

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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.

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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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