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.

f(x) = _________, where x = 2, 4, 6, 10

Answer 1

To construct a probability model for the experiment of picking a card from the numbers 2, 4, 6, and 10, we first note that there are 4 equally likely outcomes. The probability of each outcome (picking one of the cards) can be calculated using the formula:

\[
P(X = x) = \frac{1}{n}
\]

where \( n \) is the total number of outcomes.

In this case, we have \( n = 4 \) (the cards 2, 4, 6, and 10). Therefore, the probability of each card is:

\[
P(X = 2) = \frac{1}{4}
\]
\[
P(X = 4) = \frac{1}{4}
\]
\[
P(X = 6) = \frac{1}{4}
\]
\[
P(X = 10) = \frac{1}{4}
\]

We can write the probability model as:

\[
f(x) = \frac{1}{4}, \quad \text{for } x = 2, 4, 6, 10
\]

Thus, the final answer is:

\[
f(x) = \frac{1}{4}, \text{ where } x = 2, 4, 6, 10
\]