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 x=2, 4, 6, 10
Answers
GPT-4o mini
To create a probability model for the given experiment of picking a card from the number cards 2, 4, 6, and 10, we first need to assign probabilities to each outcome.
Since there are four card outcomes (2, 4, 6, and 10) and each outcome is equally likely, the probability \( P(x) \) of picking any specific card \( x \) is given by:
\[
P(x) = \frac{1}{\text{total outcomes}} = \frac{1}{4}
\]
We can write the probability model in the form of a function \( f(x) \) as follows:
\[
f(x) =
\begin{cases}
\frac{1}{4} & \text{if } x = 2, 4, 6, 10 \\
0 & \text{otherwise}
\end{cases}
\]
Thus, the probability model is:
\[
f(x) = \frac{1}{4}, \quad \text{for } x = 2, 4, 6, 10
\]
This indicates a uniform distribution over the four outcomes.
Since there are four card outcomes (2, 4, 6, and 10) and each outcome is equally likely, the probability \( P(x) \) of picking any specific card \( x \) is given by:
\[
P(x) = \frac{1}{\text{total outcomes}} = \frac{1}{4}
\]
We can write the probability model in the form of a function \( f(x) \) as follows:
\[
f(x) =
\begin{cases}
\frac{1}{4} & \text{if } x = 2, 4, 6, 10 \\
0 & \text{otherwise}
\end{cases}
\]
Thus, the probability model is:
\[
f(x) = \frac{1}{4}, \quad \text{for } x = 2, 4, 6, 10
\]
This indicates a uniform distribution over the four outcomes.