To create a probability model for the given experiment of picking a card from the numbers 2, 4, 6, and 10, we first note that there are 4 cards, and each card is equally likely to be chosen.
The probability \( f(x) \) for each value \( x \) in the sample space must sum to 1. Since all outcomes are equally likely, the probability of each individual outcome is:
\[ f(x) = \frac{1}{\text{number of outcomes}} = \frac{1}{4} \]
Thus, for each value of \( x \) (which can be 2, 4, 6, or 10), we can write:
\[ f(x) = \frac{1}{4}, \quad \text{for } x = 2, 4, 6, 10 \]
So the complete answer in equation form is:
\[ f(x) = \frac{1}{4}, \text{ where } x = 2, 4, 6, 10 \]