Identifying the Sample Space of a Probability Experiment In Exercises 25-32, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate.
28. Identifying a person's eye color (brown, blue, green, hazel, gray, other) and hair color (black, brown, blonde, red, other).

Verified step by step guidance

1. Step 1: Understand the problem. The task is to identify the sample space of a probability experiment where we are observing two characteristics: eye color and hair color. The possible outcomes are all combinations of eye colors and hair colors.
2. Step 2: List the possible outcomes for each characteristic. For eye color, the possible outcomes are {brown, blue, green, hazel, gray, other}. For hair color, the possible outcomes are {black, brown, blonde, red, other}.
3. Step 3: Use the rule of multiplication to determine the total number of outcomes in the sample space. Multiply the number of eye color options (6) by the number of hair color options (5). This gives the total number of combinations.
4. Step 4: Construct the sample space by pairing each eye color with each hair color. For example, one outcome is (brown eyes, black hair), another is (blue eyes, brown hair), and so on. Write out all possible pairs.
5. Step 5: Draw a tree diagram to visually represent the sample space. Start with a branch for each eye color, and from each eye color branch, draw branches for each hair color. This will help visualize all possible combinations.

Key Concepts

Sample Space

The sample space is the set of all possible outcomes of a probability experiment. In the context of the given question, it includes all combinations of eye color and hair color. Understanding the sample space is crucial for calculating probabilities and analyzing outcomes in experiments.

Outcomes

Outcomes are the individual results that can occur from a probability experiment. For the eye and hair color example, each unique combination of eye color and hair color represents a distinct outcome. Counting the total number of outcomes helps in determining the size of the sample space.

Tree Diagram

A tree diagram is a visual representation used to illustrate all possible outcomes of a probability experiment. It branches out from a starting point, showing each choice and its subsequent outcomes. In this case, a tree diagram can effectively display the combinations of eye and hair colors, making it easier to visualize the sample space.