Question

Zachary rolls this die once and picks one marble from a bag. The bag has 1 blue marble and 1 red marble.

Which tree diagram represents the sample space of this compound event?

Answer 1

To represent the sample space of Zachary's compound event (rolling a die and picking a marble), we can create a tree diagram with two stages: the first stage for the die roll and the second stage for picking a marble from the bag.

### Step-by-step Tree Diagram:

1. **First Stage: Rolling the Die**
- The die has 6 faces, so there will be 6 branches for this stage:
- 1
- 2
- 3
- 4
- 5
- 6

2. **Second Stage: Picking a Marble**
- From each outcome of the die roll, there are 2 possible outcomes for picking a marble: Blue (B) or Red (R).

### Complete Tree Diagram:
- Starting from the top (the roll of the die), we can list out the branches:
- For outcome "1":
- 1B (Blue marble)
- 1R (Red marble)
- For outcome "2":
- 2B
- 2R
- For outcome "3":
- 3B
- 3R
- For outcome "4":
- 4B
- 4R
- For outcome "5":
- 5B
- 5R
- For outcome "6":
- 6B
- 6R

### Sample Space Representation:
The sample space can be listed as:
- {1B, 1R, 2B, 2R, 3B, 3R, 4B, 4R, 5B, 5R, 6B, 6R}

This tree diagram represents all the possible outcomes of rolling the die and picking a marble from the bag, capturing the entire sample space for the compound event.