To create a probability model for the experiment of picking a card from the number cards 2, 4, 6, and 10, we first note that there are 4 cards, and the selection of each card is equally likely.
To represent the probability of drawing each card, we follow these steps:
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Identify the total number of outcomes. Here, we have 4 possible outcomes (2, 4, 6, and 10).
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Since each outcome is equally likely, the probability of selecting any one of these numbers is given by the formula:
\[ P(x) = \frac{1}{\text{Total Outcomes}} = \frac{1}{4} \]
This probability applies to each card. Therefore, we write the probability function as follows:
\[ f(x) = \frac{1}{4}, \quad \text{for } x = 2, 4, 6, 10 \]
So the probability model for this experiment can be summarized as:
\[ f(x) = \begin{cases} \frac{1}{4} & \text{if } x = 2 \ \frac{1}{4} & \text{if } x = 4 \ \frac{1}{4} & \text{if } x = 6 \ \frac{1}{4} & \text{if } x = 10 \ 0 & \text{otherwise} \end{cases} \]
This model reflects that each card has a probability of \(\frac{1}{4}\) of being drawn.