To create a probability model for the experiment of picking a card from a selection of cards numbered 5, 10, and 15, we need to determine the probability associated with each card.
Assuming that each card has an equal probability of being selected, we distribute the total probability (1) equally among the 3 cards. The probabilities for each card would be:
- Probability of picking card numbered 5: \( P(X = 5) = \frac{1}{3} \)
- Probability of picking card numbered 10: \( P(X = 10) = \frac{1}{3} \)
- Probability of picking card numbered 15: \( P(X = 15) = \frac{1}{3} \)
This can be expressed as a probability mass function (pmf), denoted by \( f(x) \):
\[ f(x) = \begin{cases} \frac{1}{3} & \text{if } x = 5 \ \frac{1}{3} & \text{if } x = 10 \ \frac{1}{3} & \text{if } x = 15 \ 0 & \text{otherwise} \end{cases} \]
In summary, the equation can be stated as:
- \( f(x) = \frac{1}{3} \) for \( x = 5, 10, 15 \)
List of values of \( x \) in ascending order:
- \( x = 5, 10, 15 \)