To define a probability model for the experiment of picking a card numbered 5, 10, or 15, we first determine the possible outcomes and their associated probabilities.
In this case, the outcomes are the numbers on the cards: 5, 10, and 15. We assume each card has an equal probability of being chosen. Since there are three cards, the probability of selecting each card is:
\[ P(5) = \frac{1}{3}, \quad P(10) = \frac{1}{3}, \quad P(15) = \frac{1}{3} \]
The probability mass function \(f(x)\) can be written 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, we can list the values of \(x\) in ascending order:
\[ x = 5, 10, 15 \]
In conclusion, the probability model can be summarized as follows:
-
Probability model: ( 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} )
-
Values of x: \( x = 5, 10, 15 \)