Question

n experiment involves picking a card from the number cards 2, 4, 6, 10
. In equation form. What is the probability model for this experiment? Write your answer in the simplest form of a fraction.(1 point)
f(x)=

, where x=2, 4, 6, 10

Answer 1

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 possible outcomes. Since each outcome (card) is equally likely, the probability of picking each card will be the same.

The probability of each outcome can be calculated as follows:

\[
P(X = x) = \frac{1}{\text{Number of outcomes}} = \frac{1}{4}
\]

Thus, the probability model (function) \( f(x) \) can be expressed as:

\[
f(x) =
\begin{cases}
\frac{1}{4} & \text{if } x = 2 \\
\frac{1}{4} & \text{if } x = 4 \\
\frac{1}{4} & \text{if } x = 6 \\
\frac{1}{4} & \text{if } x = 10 \\
0 & \text{otherwise}
\end{cases}
\]

In simpler notation, we can summarize the probability model as:

\[
f(x) = \frac{1}{4} \quad \text{for } x \in \{2, 4, 6, 10\}
\]

And \( f(x) = 0 \) for any other values of \( x \).