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.

Answer 1

To determine the probability model for the experiment of picking a card from the number cards 2, 4, 6, and 10, we first note the total number of outcomes. In this case, there are 4 possible outcomes (the cards) to choose from: 2, 4, 6, and 10.

Assuming that each card has an equal likelihood of being chosen, the probability of picking any specific card can be calculated using the formula:

\[
P(\text{each card}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]

Since there is only one favorable outcome for picking each card and there are 4 cards total, we can compute the probability for each card as follows:

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

Thus, the probability model for this experiment can be summarized as follows:

- \( P(2) = \frac{1}{4} \)
- \( P(4) = \frac{1}{4} \)
- \( P(6) = \frac{1}{4} \)
- \( P(10) = \frac{1}{4} \)

This means the probability model for picking a card from the set {2, 4, 6, 10} is:

\[
\left\{
\begin{array}{ll}
P(2) = \frac{1}{4} \\
P(4) = \frac{1}{4} \\
P(6) = \frac{1}{4} \\
P(10) = \frac{1}{4}
\end{array}
\right.
\]