To create a probability model for the experiment of picking a card from the number cards 2, 4, 6, and 10, we first need to calculate the probabilities of selecting each card.
Since there are 4 cards and we assume each card has an equal probability of being chosen, the probability of picking each card is:
\[ P(X = x) = \frac{1}{n} \]
where \( n \) is the number of cards.
In this case, \( n = 4 \). Thus, the probability for each card is:
\[ P(X = 2) = \frac{1}{4}, \quad P(X = 4) = \frac{1}{4}, \quad P(X = 6) = \frac{1}{4}, \quad P(X = 10) = \frac{1}{4} \]
So, the probability model can be expressed as:
\[ f(x) = \begin{cases} \frac{1}{4} & \text{if } x \in {2, 4, 6, 10} \ 0 & \text{otherwise} \end{cases} \]
In simpler terms, we can write:
\[ f(x) = \begin{cases} \frac{1}{4} & \text{for } x = 2, 4, 6, 10 \ 0 & \text{for other values of } x \end{cases} \]
This function describes the probability distribution of the random variable \( X \) representing the outcome of the experiment.