Probabilities are numbers that represent the likelihood of an event occurring. They must meet the following conditions:

1. Probabilities must be greater than or equal to 0.
2. Probabilities must be less than or equal to 1.

Let’s evaluate the given values against these conditions:

• 1: This is a valid probability (since 1 is the maximum possible probability).
• √2 ≈ 1.414: This is greater than 1, so it cannot be a probability.
• 0: This is a valid probability (since probabilities can be 0).
• 3/5 = 0.6: This is between 0 and 1, so it is a valid probability.
• 5/3 ≈ 1.6667: This is greater than 1, so it cannot be a probability.
• 0.05: This is between 0 and 1, so it is a valid probability.
• -0.58: This is less than 0, so it cannot be a probability.
• 1.13: This is greater than 1, so it cannot be a probability.

The values that cannot be probabilities are:

• √2 (C)
• 5/3 (F)
• -0.58 (D)
• 1.13 (B)

Would you like further explanation or details on these concepts?

5 Related Questions:

1. What is the difference between theoretical and experimental probability?
2. Can a probability be exactly 0 or 1? What do these values represent?
3. How do you calculate the probability of multiple independent events?
4. What is the probability of an impossible event?
5. How can you use probability in real-life decision-making?

Tip:

When dealing with probabilities, always ensure the value is within the range [0, 1]. If it's outside this range, it's not a valid probability.