To create a probability model for an experiment involving picking cards numbered 5, 10, and 15, we first identify the possible outcomes and assign probabilities to each outcome. Assuming each card has an equal chance of being picked, we can express the probability model as follows:
Let \( f(x) \) denote the probability of picking each card.
The possible values of \( x \) (the values on the cards) are 5, 10, and 15.
Since each card has an equal chance of being drawn, the probabilities are:
- \( P(X = 5) = \frac{1}{3} \)
- \( P(X = 10) = \frac{1}{3} \)
- \( P(X = 15) = \frac{1}{3} \)
Thus, the probability function can be expressed as:
\[ f(x) = \frac{1}{3}, \text{ for } x = 5, 10, 15 \]
So, our answers would be:
- \( f(x) = \frac{1}{3} \)
- \( x = 5, 10, 15 \) (in ascending order)
Final answer:
\[ f(x) = \frac{1}{3}, \text{ where } x = 5, 10, 15 \]