Figure 6.7 displays several assignments of probability to the six faces of a die. We can learn which assignment is actually accurate for a particular die only by rolling the die many times. However, some of the asssignments are not legitimate assignments of probabliity. That is, they do not obey the rules. Which are legitimate and which are not? In the case of the illegitimate models, explain what is wrong. (Select all that apply.) Outcome Model 1 Model 2 Model 3 Model 4 1 7 国 Figure 6.7 Four assignmetns of probability to the six faces of a die. Model 1: There are repeated probabilities. O There are 0 probabilities. O There are negative probabilities. O The probabilities have a sum not equal to 1. O This model is legitimate. Model 2: There are repeated probabilities. O There are 0 probabilities. O There are negative probabilities. O The probabilities have a sum not equal to 1. O This model is legitimate. Model 3: There are repeated probabilities. O There are 0 probabilities. O There are negative probabilities. The probabilities have a sum not equal to 1. O This model is legitimate. -131131/ 116-13-3 16 1161611616 113 16 113

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**Title: Evaluating Probability Assignments for a Die**

**Introduction:**
In the study of probability, it's crucial to ensure that probability assignments are legitimate. That is, they must conform to the established rules of probability. In this example, we will examine four different models that assign probabilities to the faces of a six-sided die. By analyzing these models, we can determine which are accurate representations and which contain errors.

**Figure Explanation:**

**Figure 6.7: Four assignments of probability to the six faces of a die.**
- **Outcome:** This row shows the faces of a die from 1 to 6.
- **Models:**
  - **Model 1, 2, 3, and 4:** These columns list the probabilities assigned to each face under different models.

Below is the table data:

| Outcome | Model 1 | Model 2 | Model 3 | Model 4 |
|---------|---------|---------|---------|---------|
| 1       | 1/3     | 1/6     | 1/7     | 1/3     |
| 2       | 1/3     | 1/6     | 1/7     | 1/3     |
| 3       | 0       | 1/6     | 1/7     | -1/6    |
| 4       | 1/6     | 1/6     | 1/7     | 1/3     |
| 5       | 1/6     | 1/6     | 1/7     | -1/6    |
| 6       | 1/6     | 1/6     | 1/7     | 1/3     |

**Assessment Checklist:**

**Model 1:**
⬜ There are repeated probabilities.  
⬜ There are 0 probabilities.  
⬜ There are negative probabilities.  
⬜ The probabilities have a sum not equal to 1.  
⬜ This model is legitimate.  

**Model 2:**
⬜ There are repeated probabilities.  
⬜ There are 0 probabilities.  
⬜ There are negative probabilities.  
⬜ The probabilities have a sum not equal to 1.  
⬜ This model is legitimate.  

**Model 3:**
⬜ There are repeated probabilities.  
⬜ There
Transcribed Image Text:--- **Title: Evaluating Probability Assignments for a Die** **Introduction:** In the study of probability, it's crucial to ensure that probability assignments are legitimate. That is, they must conform to the established rules of probability. In this example, we will examine four different models that assign probabilities to the faces of a six-sided die. By analyzing these models, we can determine which are accurate representations and which contain errors. **Figure Explanation:** **Figure 6.7: Four assignments of probability to the six faces of a die.** - **Outcome:** This row shows the faces of a die from 1 to 6. - **Models:** - **Model 1, 2, 3, and 4:** These columns list the probabilities assigned to each face under different models. Below is the table data: | Outcome | Model 1 | Model 2 | Model 3 | Model 4 | |---------|---------|---------|---------|---------| | 1 | 1/3 | 1/6 | 1/7 | 1/3 | | 2 | 1/3 | 1/6 | 1/7 | 1/3 | | 3 | 0 | 1/6 | 1/7 | -1/6 | | 4 | 1/6 | 1/6 | 1/7 | 1/3 | | 5 | 1/6 | 1/6 | 1/7 | -1/6 | | 6 | 1/6 | 1/6 | 1/7 | 1/3 | **Assessment Checklist:** **Model 1:** ⬜ There are repeated probabilities. ⬜ There are 0 probabilities. ⬜ There are negative probabilities. ⬜ The probabilities have a sum not equal to 1. ⬜ This model is legitimate. **Model 2:** ⬜ There are repeated probabilities. ⬜ There are 0 probabilities. ⬜ There are negative probabilities. ⬜ The probabilities have a sum not equal to 1. ⬜ This model is legitimate. **Model 3:** ⬜ There are repeated probabilities. ⬜ There
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