Which of the following values cannot be​ probabilities?
0.02​, 5 divided by 3​, 0​, StartRoot 2 EndRoot​, 3 divided by 5​, negative 0.42​, 1​, 1.48
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Part 1
Select all the values that cannot be probabilities.
A.0
0
B.StartRoot 2 EndRoot
StartRoot 2 EndRoot
C.1
1
D.three fifths
three fifths
E.negative 0.42
negative 0.42
F.five thirds
five thirds
G.1.48
1.48
H.0.02
0.02

To determine which of the given values cannot be probabilities, we need to recall that probabilities must lie between 0 and 1, inclusive. This means that any probability value \( P \) must satisfy the inequality \( 0 \leq P \leq 1 \).

Let's evaluate each value:

1. **0.02**: This value lies between 0 and 1, so it **can** be a probability.
2. **\(\frac{5}{3}\)**: This value is greater than 1 (approximately 1.67), so it **cannot** be a probability.
3. **0**: This value is equal to the lower bound of the interval, so it **can** be a probability.
4. **\(\sqrt{2}\)**: The square root of 2 is approximately 1.414, which is greater than 1, so it **cannot** be a probability.
5. **\(\frac{3}{5}\)**: This value lies between 0 and 1 (0.6), so it **can** be a probability.
6. **-0.42**: This value is less than 0, so it **cannot** be a probability.
7. **1**: This value is equal to the upper bound of the interval, so it **can** be a probability.
8. **1.48**: This value is greater than 1, so it **cannot** be a probability.

Based on the above evaluations, the values that cannot be probabilities are:
- \(\frac{5}{3}\)
- \(\sqrt{2}\)
- -0.42
- 1.48

Therefore, the correct selections are:
B. \(\sqrt{2}\)
E. -0.42
F. \(\frac{5}{3}\)
G. 1.48

Would you like more details or have any questions?

Here are 8 related questions to expand on this topic:

1. What is the definition of a probability?
2. How can probabilities be represented on a number line?
3. Can a probability ever be negative?
4. What is the sum of probabilities in a complete probability distribution?
5. How do you interpret a probability of 0?
6. How do you interpret a probability of 1?
7. What are some common misconceptions about probabilities?
8. How can probabilities be used in real-life situations?

**Tip:** When dealing with probabilities, always ensure the values are within the range [0, 1] to correctly represent the likelihood of events.

Explore which values cannot be probabilities by understanding fundamental concepts in probability theory. Learn about the range of probability values and examples of values that do not fit within this range.

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