Which of the following are probabilities ? 1, 7/2, 325%, 0.384, 0, 2.1777, 9:1, 2/7, -0.25, 50-50, 8:3

To determine which of the given values are probabilities, we need to recall that a probability is a number between 0 and 1 (inclusive). This means it can be 0 (representing an impossible event) or 1 (representing a certain event), or any number in between. Percentages can also be probabilities if they fall between 0% and 100%.

Let's evaluate each of the provided values:

1. **1**: This is a valid probability. It represents a certain event.
2. **7/2 (3.5)**: This is not a probability because it is greater than 1.
3. **325%**: This is not a probability because it is greater than 100%.
4. **0.384**: This is a valid probability because it is between 0 and 1.
5. **0**: This is a valid probability. It represents an impossible event.
6. **2.1777**: This is not a probability because it is greater than 1.
7. **9:1**: This represents odds, not a probability. To convert odds to probability:  
   \[
   P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} = \frac{9}{9+1} = \frac{9}{10} = 0.9 
   \]  
   This is a valid probability.
8. **2/7**: This is a valid probability because it is between 0 and 1.
9. **-0.25**: This is not a probability because it is negative.
10. **50-50**: This phrase is typically interpreted as 50%, which corresponds to 0.5, a valid probability.
11. **8:3**: This represents odds, not a probability. To convert odds to probability:  
   \[
   P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} = \frac{8}{8+3} = \frac{8}{11} \approx 0.727 
   \]  
   This is a valid probability.

### Summary
The valid probabilities among the provided values are:
- **1**
- **0.384**
- **0**
- **9:1** (converted to 0.9)
- **2/7**
- **50-50** (interpreted as 0.5)
- **8:3** (converted to approximately 0.727)

### Would you like more details or have any questions? 

### Related Questions
1. How do you convert percentages to probabilities?
2. How can we convert odds to probabilities?
3. What is the difference between odds and probability?
4. Why can probabilities not be negative?
5. How are probabilities used in real-life situations?

**Tip:** Always ensure probabilities are within the 0 to 1 range to correctly interpret statistical data.

Which of the following are probabilities? 1, 7/2, 325%, 0.384, 0, 2.1777, 9:1, 2/7, -0.25, 50-50, 8:3

Explore which values can be considered valid probabilities. This detailed solution walks through percentages, fractions, and odds, converting them into probabilities where applicable. Learn key formulas and concepts such as converting odds to probabilities and understanding the limits of probabilities (0 to 1). Suitable for students in Grades 6-8.

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