Question

Lucas spins this spinner once and picks one marble out of a bag. The bag has 1 yellow marble and 1 red marble.

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

Answer 1

To create a tree diagram for Lucas's compound event involving spinning a spinner and picking a marble, we need to account for both actions and their possible outcomes.

1. **First Action - Spinning the Spinner**: Assume the spinner has outcomes labeled as A and B (if the spinner has more outcomes, you would need to include those as well). For simplicity, let's say:

- **Outcome 1**: A
- **Outcome 2**: B

2. **Second Action - Picking a Marble**: Lucas can pick either:
- Yellow (Y)
- Red (R)

Now, we can construct the tree diagram:

1. Start with a single point representing the initial state before spinning the spinner.

2. From that point, draw branches for the spinner outcomes:
- One branch for outcome A
- Another branch for outcome B

3. From each of those branches for A and B, draw two branches representing the outcomes from picking a marble:
- From A: One branch for Yellow (A, Y) and another branch for Red (A, R).
- From B: One branch for Yellow (B, Y) and another branch for Red (B, R).

Putting it all together, your tree diagram will look like this:

```
Start
/ \
A B
/ \ / \
Y R Y R
```

The resulting sample space from this tree diagram would be:
- (A, Y)
- (A, R)
- (B, Y)
- (B, R)

This represents all possible outcomes of the compound event.