To create a probability model for an experiment involving cards numbered 5, 10, and 15, we define the random variable \( x \) as the numbers on the cards. The probability model assigns a probability to each possible outcome.
Assuming the cards are picked randomly and each card has an equal chance of being chosen, the probability for each card is:
- For card numbered 5: \( P(x = 5) = \frac{1}{3} \)
- For card numbered 10: \( P(x = 10) = \frac{1}{3} \)
- For card numbered 15: \( P(x = 15) = \frac{1}{3} \)
The probability model can be written as follows:
\[ f(x) = \begin{cases} \frac{1}{3} & \text{if } x = 5 \ \frac{1}{3} & \text{if } x = 10 \ \frac{1}{3} & \text{if } x = 15 \ 0 & \text{otherwise} \end{cases} \]
The values of \( x \) in ascending order are:
\[ x = 5, 10, 15 \]
So, the final answers are:
- \( f(x) = \) as described above
- \( x = 5, 10, 15 \)