Question

An experiment involves picking a card from a selection of cards numbered 5, 10, and 15. In equation form, what is the probability model for this experiment? List the values of x in ascending order.(2 points)
f(x)=
, where x=
,
,

Answer 1

To create a probability model for an experiment involving cards numbered 5, 10, and 15, we define the random variable \( x \) as the numbers on the cards. The probability model assigns a probability to each possible outcome.

Assuming the cards are picked randomly and each card has an equal chance of being chosen, the probability for each card is:

- For card numbered 5: \( P(x = 5) = \frac{1}{3} \)
- For card numbered 10: \( P(x = 10) = \frac{1}{3} \)
- For card numbered 15: \( P(x = 15) = \frac{1}{3} \)

The probability model can be written as follows:

\[
f(x) =
\begin{cases}
\frac{1}{3} & \text{if } x = 5 \\
\frac{1}{3} & \text{if } x = 10 \\
\frac{1}{3} & \text{if } x = 15 \\
0 & \text{otherwise}
\end{cases}
\]

The values of \( x \) in ascending order are:

\[
x = 5, 10, 15
\]

So, the final answers are:
- \( f(x) = \) as described above
- \( x = 5, 10, 15 \)