Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram. Determining a person's entree (steak \( (\mathrm{S}) \), chicken \( (\mathrm{C}) \), pork \( (\mathrm{P})) \) and then their vegetable (corn (C), broccoli (B)) Identify the sample space. A. \( \{\mathrm{SC}, \mathrm{SB}, \mathrm{CC}, \mathrm{CB}, \mathrm{PC}, \mathrm{PB}\} \) B. \( \{\mathrm{SC}, \mathrm{SB}, \mathrm{CC}, \mathrm{CB}, \mathrm{PC}, \mathrm{PB}, \mathrm{PC}, \mathrm{PB}\} \) C. \( \{\mathrm{SC}, \mathrm{SB}, \mathrm{SC}, \mathrm{CC}, \mathrm{CB}, \mathrm{CC}, \mathrm{PC}, \mathrm{PB}, \mathrm{PC}\} \) D. \( \{\mathrm{SC}, \mathrm{SB}, \mathrm{CC}, \mathrm{CB}, \mathrm{PC}, \mathrm{PB}, \mathrm{PC}, \mathrm{PB}, \mathrm{SC}, \mathrm{SB}\} \)

The sample space of a probability experiment represents all possible outcomes. In this case, the experiment involves two sequential choices: 1. **Choosing an Entree:** - Steak (S) - Chicken (C) - Pork (P) 2. **Choosing a Vegetable:** - Corn (C) - Broccoli (B) To determine the sample space, we consider all possible ordered pairs of entree and vegetable combinations: - **Steak with Corn:** SC - **Steak with Broccoli:** SB - **Chicken with Corn:** CC - **Chicken with Broccoli:** CB - **Pork with Corn:** PC - **Pork with Broccoli:** PB Thus, the sample space is: \[ \{\mathrm{SC}, \mathrm{SB}, \mathrm{CC}, \mathrm{CB}, \mathrm{PC}, \mathrm{PB}\} \] **Number of Outcomes:** There are 3 choices for the entree and 2 choices for the vegetable, leading to: \[ 3 \times 2 = 6 \text{ outcomes} \] **Tree Diagram:** ``` Start ├── S (Steak) │ ├── C (Corn) → SC │ └── B (Broccoli) → SB ├── C (Chicken) │ ├── C (Corn) → CC │ └── B (Broccoli) → CB └── P (Pork) ├── C (Corn) → PC └── B (Broccoli) → PB ``` **Correct Option:** **A.** \( \{\mathrm{SC}, \mathrm{SB}, \mathrm{CC}, \mathrm{CB}, \mathrm{PC}, \mathrm{PB}\} \) Answer: Option A