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8.1 Assigning a Measure to Likelihood

8.1 Assigning a Measure to Likelihood
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  • 21. Comparing Events

    You spin spinner A. Which event has a greater likelihood? Explain your reasoning.

    1. Event 1: Spinning a number less than 1

      Event 2: Spinning a number greater than 1

    2. Event 1: Spinning a multiple of 3

      Event 2: Spinning a number greater than 3

    • Worked-Out Solution
      1. Event 2 has a greater likelihood because there are 5 numbers that are greater than 1 on the spinner.
      2. There are only 2 multiples of 3. There are 3 numbers that are greater than 3. So, Event 2 is more likely.
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      ______    ______             __   __  __    __  
     /_   _//  /_   _//   ____     \ \\/ // \ \\ / // 
       | ||     -| ||-   |    \\    \ ` //   \ \/ //  
      _| ||     _| ||_   | [] ||     | ||     \  //   
     /__//     /_____//  |  __//     |_||      \//    
     `--`      `-----`   |_|`-`      `-`'       `     
                         `-`                          
    
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  • 22. Comparing Events

    You spin spinner B. Which event has a greater likelihood? Explain your reasoning.

    1. Event 1: Spinning green

      Event 2: Spinning red

    2. Event 1: Spinning an even number

      Event 2: Spinning a prime number

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      ______     ___                 ___      _  _   
     /_   _//   / _ \\    ____      / _ \\   | \| || 
       | ||    | / \ ||  |    \\   | / \ ||  |  ' || 
      _| ||    | \_/ ||  | [] ||   | \_/ ||  | .  || 
     /__//      \___//   |  __//    \___//   |_|\_|| 
     `--`       `---`    |_|`-`     `---`    `-` -`  
                         `-`                         
    
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  • 23. Comparing Events

    You spin both spinners. Which event has a greater likelihood? Explain your reasoning.

    1. Event 1: Spinning blue on spinner A

      Event 2: Spinning blue on spinner B

    2. Event 1: Spinning a multiple of 2 on spinner A

      Event 2: Spinning a mulitple of 6 on spinner B

    • Worked-Out Solution
      1. There are 2 blue areas on Spinner A. There are 3 blue areas on Spinner B. So, Event 2 is more likely.
      2. There are 3 multiples of 2 on spinner A. There is only 1 multiple of 6 on spinner B. So, Event 1 is more likely.
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                _____     _____      ___      _____   
      ____     |  ___||  /  ___||   / _ \\   /  ___|| 
     |    \\   | ||__   | // __    | / \ || | // __   
     | [] ||   | ||__   | \\_\ ||  | \_/ || | \\_\ || 
     |  __//   |_____||  \____//    \___//   \____//  
     |_|`-`    `-----`    `---`     `---`     `---`   
     `-`                                              
    
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  • 24. Impossible and Certain Events

    Describe two events that are impossible. Describe two events that are certain. Explain your reasoning.

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