To create a probability model for the experiment of picking a card from a selection of cards numbered 5, 10, and 15, we first define the probability function \( f(x) \) for the outcomes in the experiment.
Since we have three outcomes (the cards numbered 5, 10, and 15), we can define \( f(x) \) as follows:
- The function \( f(x) \) gives the probability of each outcome.
- Assuming that each card is equally likely to be picked, each outcome has the same probability.
So, we can set up the probability model as: \[ f(x) = \frac{1}{3} \]
for each of the values of \( x \).
The values of \( x \) are the outcomes of the experiment (the numbers on the cards), which are:
- \( 5 \)
- \( 10 \)
- \( 15 \)
In ascending order, the values of \( x \) are: \[ x = 5, 10, 15 \]
Putting it all together:
\[ f(x) = \frac{1}{3} \text{ for } x = 5, 10, 15 \]