### 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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```   _____     ___       _____     ___     _    _
/ ___//   / _ \\    / ___//   / _ \\  | || | ||
\___ \\  / //\ \\   \___ \\  / //\ \\ | || | ||
/    // |  ___  ||  /    // |  ___  ||| \\_/ ||
/____//  |_||  |_|| /____//  |_||  |_|| \____//
`-----`   `-`   `-` `-----`   `-`   `-`   `---`

```