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 possible outcomes of the experiment and assign probabilities to each of them.
Step 1: Define the Values of \( x \)
The values associated with the cards are:
- \( x_1 = 5 \)
- \( x_2 = 10 \)
- \( x_3 = 15 \)
Arranging these in ascending order gives:
- \( x = 5, 10, 15 \)
Step 2: Define the Probability Distribution \( f(x) \)
Assuming each card is equally likely to be picked, the probability for each card will be the same. Since there are three cards, the probability for each card is:
\[ f(x) = \frac{1}{3} \]
Final Model
Thus, we can express the probability model as follows:
\[ f(x) = \begin{cases} \frac{1}{3} & \text{for } x = 5 \ \frac{1}{3} & \text{for } x = 10 \ \frac{1}{3} & \text{for } x = 15 \ 0 & \text{otherwise} \end{cases} \]
Answer:
- \( f(x) = \frac{1}{3} \), where \( x = 5, 10, 15 \)