To create a probability model for the experiment of picking a card from a selection of cards numbered 5, 10, and 15, we first need to determine the probabilities associated with each outcome.
Assuming each card has an equal chance of being selected, the probability model can be defined as follows:
- The possible values of \( x \) are the numbers on the cards.
- The cards are numbered 5, 10, and 15.
Thus, the probability for each card would be:
\[ f(x) = \frac{1}{3} \quad \text{for each value of } x \]
This is because there are 3 cards, and each card has an equal probability of being selected.
In equation form, we can express the probability model as:
\[ f(x) = \begin{cases} \frac{1}{3} & \text{if } x = 5 \ \frac{1}{3} & \text{if } x = 10 \ \frac{1}{3} & \text{if } x = 15 \ 0 & \text{otherwise} \end{cases} \]
Now, we can list the values of \( x \) in ascending order:
\[ x = 5, 10, 15 \]
So the final answer can be summarized as:
\[ f(x) = \frac{1}{3}, \text{ where } x = 5, 10, 15 \]