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Answer :
To determine which values can represent the probability of an event, we need to understand the range of valid probability values. A probability must be between 0 and 1, inclusive. This means any valid probability value can be 0, any value between 0 and 1, or 1.
Let's examine each of the given numbers:
1. 3.51: This value is greater than 1, so it cannot represent a probability.
2. 0.63: This value is between 0 and 1, so it is a valid probability.
3. 3.51%: To convert a percentage to a probability, we divide by 100. So, 3.51% becomes 0.0351. Since 0.0351 is between 0 and 1, it's a valid probability.
4. 1: This value is exactly 1, which is a valid probability.
5. 1.58: This value is greater than 1, so it is not a valid probability.
6. 150%: Converting this to a probability involves dividing by 100, giving 1.5. Since 1.5 is greater than 1, it cannot be a valid probability.
7. 0: This value is exactly 0, which is a valid probability.
8. [tex]\(\frac{6}{7}\)[/tex]: This fraction equals approximately 0.8571, which is between 0 and 1, making it a valid probability.
Based on this analysis, the values that can represent the probability of an event are: 0.63, 0.0351, 1, 0, and approximately 0.8571 (from the fraction [tex]\(\frac{6}{7}\)[/tex]).
Let's examine each of the given numbers:
1. 3.51: This value is greater than 1, so it cannot represent a probability.
2. 0.63: This value is between 0 and 1, so it is a valid probability.
3. 3.51%: To convert a percentage to a probability, we divide by 100. So, 3.51% becomes 0.0351. Since 0.0351 is between 0 and 1, it's a valid probability.
4. 1: This value is exactly 1, which is a valid probability.
5. 1.58: This value is greater than 1, so it is not a valid probability.
6. 150%: Converting this to a probability involves dividing by 100, giving 1.5. Since 1.5 is greater than 1, it cannot be a valid probability.
7. 0: This value is exactly 0, which is a valid probability.
8. [tex]\(\frac{6}{7}\)[/tex]: This fraction equals approximately 0.8571, which is between 0 and 1, making it a valid probability.
Based on this analysis, the values that can represent the probability of an event are: 0.63, 0.0351, 1, 0, and approximately 0.8571 (from the fraction [tex]\(\frac{6}{7}\)[/tex]).
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