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.
f (x)=blank, where x= blank, blank, blank

Answer 1

In this experiment, you are selecting a card from a set of cards numbered 5, 10, and 15. To set up a probability model, we first need to define the random variable \( x \) which represents the card number drawn.

The probability model can be represented as a function \( f(x) \) where \( f(x) \) gives the probability of drawing each card.

Assuming that each card is equally likely to be drawn, we have:

1. The possible values of \( x \) are 5, 10, and 15.
2. Each of these values has an equal probability of \( \frac{1}{3} \) since there are three cards.

Thus, the probability model can be expressed as:

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

So, in equation form:

\[
f(x) = \frac{1}{3}, \text{ where } x = 5, 10, 15
\]

In ascending order, the values of \( x \) are:

\[
x = 5, 10, 15
\]