Tree diagram probability worksheet with spinner activity.

Since I can't view or access images directly, I’ll help you solve the problem based on the description you provided. Let's work through the task step by step.

---

Problem Description:

David has a spinner with black and white sections. He spins it twice. You're asked to:
1. Complete a tree diagram showing all possible outcomes.
2. Answer three probability questions.

Let’s assume the spinner is divided into two equal parts (50% black, 50% white), unless otherwise specified. Since no specific proportions are given in your message, we'll proceed with this common assumption.

But wait — there's a pie chart shown in the image (as mentioned in your text). It shows a circle divided into two sections: one labeled "Black" and one labeled "White". From the visual (which I can't see), let's suppose:

- The black section is 3/4 of the spinner
- The white section is 1/4

This is a common setup in such problems when the spinner is not balanced. Since the pie chart isn't visible, I’ll make an educated guess based on typical problems like this.

> ✔ Assumption:
> - P(Black) = 3/4
> - P(White) = 1/4

If your spinner looks different (e.g., half black, half white), let me know and I’ll adjust.

---

Step 1: Tree Diagram

We’re spinning the spinner twice, so the tree will have:

- First spin: Two branches → Black (3/4), White (1/4)
- Second spin: For each outcome, two more branches → Black (3/4), White (1/4)

So the full tree has four paths:

1. Black → Black
2. Black → White
3. White → Black
4. White → White

Now, label each branch with probabilities.

---

Tree Diagram Structure:

```
Start
├── Black (3/4)
│ ├── Black (3/4) → P = (3/4) × (3/4) = 9/16
│ └── White (1/4) → P = (3/4) × (1/4) = 3/16
└── White (1/4)
├── Black (3/4) → P = (1/4) × (3/4) = 3/16
└── White (1/4) → P = (1/4) × (1/4) = 1/16
```

---

Now Answer the Questions

#### a) What is the probability that David will spin black then white?

That’s the path: Black → White

P(Black then White) = P(Black) × P(White) = (3/4) × (1/4) = 3/16

✔ Answer: 3/16

---

#### b) What is the probability that David will spin white twice?

Path: White → White

P(White then White) = (1/4) × (1/4) = 1/16

✔ Answer: 1/16

---

#### c) What is the probability that David will spin the same color twice?

Two cases:
- Black then Black: (3/4)(3/4) = 9/16
- White then White: (1/4)(1/4) = 1/16

Add them:
P(Same color twice) = 9/16 + 1/16 = 10/16 = 5/8

✔ Answer: 5/8

---

Final Answers:

a) P(Black, then White) = 3/16
b) P(White, then White) = 1/16
c) P(Same color twice) = 5/8

---

How to Fill in the Tree Diagram Boxes:

On the worksheet, you’ll likely have boxes for each branch:

- First level (first spin):
- Left box: Black (3/4)
- Right box: White (1/4)

- Second level (second spin):
- From Black:
- Left: Black (3/4) → Outcome: BB → P = 9/16
- Right: White (1/4) → Outcome: BW → P = 3/16
- From White:
- Left: Black (3/4) → Outcome: WB → P = 3/16
- Right: White (1/4) → Outcome: WW → P = 1/16

Then fill in the final probabilities in the boxes at the end of each branch.

---

⚠️ Important Note:

If your spinner is equally divided (50% black, 50% white), then:

- P(Black) = 1/2, P(White) = 1/2

Then:
- a) P(Black then White) = (1/2)(1/2) = 1/4
- b) P(White twice) = (1/2)(1/2) = 1/4
- c) P(Same color) = P(BB) + P(WW) = 1/4 + 1/4 = 1/2

So please check your spinner in the image:
👉 Is it split 3/4 black and 1/4 white? Or is it half and half?

If you can describe the pie chart (e.g., “black takes up 3/4 of the circle”), I can confirm the exact values.

For now, I’ve solved it assuming 3/4 black, 1/4 white — which matches typical versions of this worksheet.

Let me know if you want me to adjust based on actual proportions!