To set up a probability model for the experiment of picking a card from the number cards 2, 4, 5, and 10, we start by noting that there are 4 possible outcomes: 2, 4, 5, and 10. Since we want to find the probability associated with each of these outcomes, we assume that each card is equally likely to be picked.
The probability \( P(x) \) for each outcome can be calculated using the formula:
\[ P(x) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, each number card has one favorable outcome, and the total number of outcomes is 4 (the number of cards).
So, the probability for each outcome (2, 4, 5, 10) would be:
\[ P(2) = P(4) = P(5) = P(10) = \frac{1}{4} \]
Now we can represent the probability model in the form of a function \( f(x) \):
\[ f(x) = \frac{1}{4}, \quad \text{for } x = 2, 4, 5, 10 \]
Thus, the answer to your question is:
\[ f(x) = \frac{1}{4}, \text{ where } x = 2, 4, 5, 10 \]