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In problem 4a, we are asked to **draw a tree diagram** to show all the possible outcomes for this experiment, where a student picks one candy from Packet 1 and then one candy from Packet 2.

### Packet 1 contains:
- **O** (Orange),
- **L** (Lemon),
- **S** (Strawberry).

### Packet 2 contains:
- **O** (Orange),
- **S** (Strawberry),
- **R** (Raspberry).

### Tree Diagram Explanation:
1. **Step 1 (Choose from Packet 1):**
   - The first branch represents the choices from Packet 1: \( O_1 \) (Orange), \( L \) (Lemon), and \( S_1 \) (Strawberry).
   
2. **Step 2 (Choose from Packet 2):**
   - For each candy picked from Packet 1, the second branch represents the choices from Packet 2: \( O_2 \) (Orange), \( S_2 \) (Strawberry), and \( R \) (Raspberry).
   
### Outcomes:
- From **O_1**: \( O_2 \), \( S_2 \), \( R \) 
- From **L**: \( O_2 \), \( S_2 \), \( R \)
- From **S_1**: \( O_2 \), \( S_2 \), \( R \)

The tree diagram shows every combination of candies picked from Packet 1 and Packet 2.

### Tree Diagram Structure:

```
      O_1
    /  |  \
  O_2  S_2  R
   |
  L
    /  |  \
  O_2  S_2  R
   |
  S_1
    /  |  \
  O_2  S_2  R
```

This represents the 9 possible outcomes:
- \( (O_1, O_2), (O_1, S_2), (O_1, R), (L, O_2), (L, S_2), (L, R), (S_1, O_2), (S_1, S_2), (S_1, R) \).

Would you like further details on this? 

Here are 5 questions related to this:
1. What is the sample space for this tree diagram?
2. How would you list the outcomes where both candies are of the same type?
3. How does the tree diagram change if we add a fourth candy to either packet?
4. What is the total number of outcomes when adding more candies to both packets?
5. How can we calculate the probability of picking two specific candies from different packets?

**Tip:** Drawing tree diagrams helps visualize complex probability problems, making it easier to calculate probabilities and sample spaces.

Learn how to draw a tree diagram to find all possible outcomes for a candy selection experiment. This problem covers key probability concepts such as sample spaces and tree diagrams. Suitable for students in Grades 6-8.

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