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Let's break down the question and solve it.

### Part A:
The problem gives us the following information about the students:
1. 50% of students bike (B), and 50% walk (W) to school.
2. 50% of students bring lunch from home (H), and 50% eat school lunch (S).
3. After school, 60% go to drama club (D), and 40% go to French club (F).

We need to determine which tree diagram properly reflects these probabilities.

- In a tree diagram, each "branch" should reflect the probability of each event. Since every decision point has two outcomes (e.g., bike or walk), we can follow the following logic:
  - **First decision**: Either bike (B) or walk (W), with equal 50% probability each.
  - **Second decision**: Bring lunch from home (H) or eat school lunch (S), again with equal 50% probabilities.
  - **Third decision**: Go to drama (D) or French club (F), with 60% and 40% probabilities respectively.

By inspecting the diagrams, **Option D** best represents this decision process. It shows:
- Biking or walking (first branches)
- Home lunch or school lunch (second branches)
- Drama or French club (third branches, with the drama side getting a bigger branch, representing 60% probability).

### Part B:
We are asked to find the probability of a student who:
- Bikes to school,
- Brings lunch from home,
- Goes to drama club.

To solve:
1. **Biking to school** has a 50% chance: \( \frac{1}{2} \).
2. **Bringing lunch from home** has a 50% chance: \( \frac{1}{2} \).
3. **Going to drama club** has a 60% chance: \( \frac{3}{5} \).

The combined probability is:
\[
\frac{1}{2} \times \frac{1}{2} \times \frac{3}{5} = \frac{3}{20}
\]

Thus, the probability is \( \frac{3}{20} \), or 0.15.

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Do you want more details, or have any questions about this solution?

Here are some related questions you might find helpful:
1. How do tree diagrams work in probability?
2. How do you calculate combined probabilities in a sequence of events?
3. Why are probabilities multiplied in sequential independent events?
4. How can we visually represent different probabilities using diagrams?
5. What are some other ways to calculate probabilities when given choices?

**Tip**: Always make sure to verify that the probabilities in each branch of a tree diagram add up to 100%, to ensure that the scenario is well-represented.

In a class, 50% of the students bike to school (B) and 50% of the students walk to school (W). In addition, 50% of the students bring lunch from home (H) and 50% of the students eat school lunch (S). After school, 60% of the students go to drama club (D) and 40% of the students go to French club (F).

Solve a probability problem using tree diagrams. Students bike or walk to school, bring lunch from home or eat school lunch, and attend drama or French club. Learn how to calculate the probability of a specific student biking, bringing lunch from home, and going to drama club.

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