Question

An 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

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 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.