Which of the following values cannot be probabilities? 1, 1.53, 0, 3 divided by 5, 0.02, negative 0.5, square root of 2 divided by 5 divided by 3.

In the realm of probability, values must adhere to specific constraints. Probabilities are defined to lie within the range of 0 to 1, inclusive. Thus, any value that falls outside this range cannot be a valid probability.

Let’s evaluate the given options:

1. 1: This is a valid probability as it represents a certainty.
2. 1.53: This exceeds 1, and therefore cannot be a valid probability.
3. 0: This is valid, indicating impossibility.
4. 3 divided by 5 (0.6): This is valid as it is between 0 and 1.
5. 0.02: This is valid, as it is also between 0 and 1.
6. negative 0.5: This is invalid because probabilities cannot be negative.
7. square root of 2 divided by 5 divided by 3: Simplifying this expression results in a value less than 1, which could potentially be valid depending on its numerical outcome, but without an exact numerical evaluation, it is not definitively ruled out.

In summary, the values that cannot be probabilities from the provided options are 1.53 and negative 0.5.