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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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