To create a probability model for the experiment of picking a card from the number cards 2, 4, 6, and 10, we first note that there are 4 possible outcomes. Since each outcome (card) is equally likely, the probability of picking each card will be the same.
The probability of each outcome can be calculated as follows:
\[ P(X = x) = \frac{1}{\text{Number of outcomes}} = \frac{1}{4} \]
Thus, the probability model (function) \( f(x) \) can be expressed as:
\[ f(x) = \begin{cases} \frac{1}{4} & \text{if } x = 2 \ \frac{1}{4} & \text{if } x = 4 \ \frac{1}{4} & \text{if } x = 6 \ \frac{1}{4} & \text{if } x = 10 \ 0 & \text{otherwise} \end{cases} \]
In simpler notation, we can summarize the probability model as:
\[ f(x) = \frac{1}{4} \quad \text{for } x \in {2, 4, 6, 10} \]
And \( f(x) = 0 \) for any other values of \( x \).