Question
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
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
There are no human answers yet.
Answered by
GPT-4o mini
To create a probability model for the experiment of picking a card from the number cards 2, 4, 6, and 10, we need to determine the probability of selecting each card.
There are 4 possible outcomes: 2, 4, 6, and 10. Assuming each card is equally likely to be chosen, the probability of selecting any one card is given by the formula:
\[
P(x) = \frac{1}{n}
\]
where \( n \) is the total number of outcomes. In this case, \( n = 4 \).
Thus, the probability for each of the cards is:
\[
P(2) = \frac{1}{4}, \quad P(4) = \frac{1}{4}, \quad P(6) = \frac{1}{4}, \quad P(10) = \frac{1}{4}
\]
We can express this probability model in equation form as follows:
\[
f(x) = \begin{cases}
\frac{1}{4} & \text{if } x = 2 \\
\frac{1}{4} & \text{if } x = 4 \\
\frac{1}{4} & \text{if } x = 6 \\
\frac{1}{4} & \text{if } x = 10 \\
0 & \text{otherwise}
\end{cases}
\]
So the probability model can be written as:
\[
f(x) = \frac{1}{4} \text{ for } x = 2, 4, 6, 10
\]
Therefore, in the simplest fraction form, the probability model is:
\[
f(x) = \frac{1}{4} \text{ for } x=2, 4, 6, 10
\]
There are 4 possible outcomes: 2, 4, 6, and 10. Assuming each card is equally likely to be chosen, the probability of selecting any one card is given by the formula:
\[
P(x) = \frac{1}{n}
\]
where \( n \) is the total number of outcomes. In this case, \( n = 4 \).
Thus, the probability for each of the cards is:
\[
P(2) = \frac{1}{4}, \quad P(4) = \frac{1}{4}, \quad P(6) = \frac{1}{4}, \quad P(10) = \frac{1}{4}
\]
We can express this probability model in equation form as follows:
\[
f(x) = \begin{cases}
\frac{1}{4} & \text{if } x = 2 \\
\frac{1}{4} & \text{if } x = 4 \\
\frac{1}{4} & \text{if } x = 6 \\
\frac{1}{4} & \text{if } x = 10 \\
0 & \text{otherwise}
\end{cases}
\]
So the probability model can be written as:
\[
f(x) = \frac{1}{4} \text{ for } x = 2, 4, 6, 10
\]
Therefore, in the simplest fraction form, the probability model is:
\[
f(x) = \frac{1}{4} \text{ for } x=2, 4, 6, 10
\]
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