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Which of the following values cannot be probabilities?

[tex]\[0, -0.58, 0.04, 1.57, \frac{5}{3}, \frac{3}{5}, \sqrt{2}, 1\][/tex]

Answer :

To determine which values cannot be probabilities, we need to understand what qualifies a value as a valid probability. Probabilities must satisfy the following conditions:

1. A probability is a number between 0 and 1, inclusive. This means a probability can be 0, 1, or any number between them.

Let's analyze each of these values:

1. 0: This is a valid probability because it is the lower limit of the range (0 to 1).

2. -0.58: This cannot be a probability because probabilities cannot be negative.

3. 0.04: This is a valid probability because it is a positive number less than 1.

4. 1.57: This cannot be a probability because it is greater than 1.

5. 5/3 (approximately 1.6667): This cannot be a probability because it is greater than 1.

6. 3/5 (approximately 0.6): This is a valid probability because it is between 0 and 1.

7. [tex]\(\sqrt{2} (approximately 1.4142)\)[/tex]: This cannot be a probability because it is greater than 1.

8. 1: This is a valid probability because it is the upper limit of the range.

Thus, the values that cannot be probabilities are: [tex]\(-0.58\)[/tex], [tex]\(1.57\)[/tex], [tex]\(5/3\)[/tex], and [tex]\(\sqrt{2}\)[/tex].

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