In this experiment, you have a selection of cards numbered 5, 10, and 15. If we want to express the probability model mathematically, we first need to define the possible values of \( x \) and their corresponding probabilities.
Let's denote the values of the cards as:
- \( x_1 = 5 \)
- \( x_2 = 10 \)
- \( x_3 = 15 \)
Assuming each card has an equal chance of being drawn (which is a common assumption in probability problems unless stated otherwise), the probability for each card can be calculated as follows:
- Total number of cards = 3
- Probability of each card = \( \frac{1}{3} \)
Thus, the probability function can be expressed 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, listing the values of \( x \) in ascending order:
- \( x = 5, 10, 15 \)
Putting it all together, we have:
\[ f(x) = \begin{cases} \frac{1}{3} & \text{if } x = 5 \ \frac{1}{3} & \text{if } x = 10 \ \frac{1}{3} & \text{if } x = 15 \ 0 & \text{otherwise} \end{cases} \]
So, the final answer is:
Values of \( x \): 5, 10, 15.