Track the frequency of dice rolls with this easy-to-use probability tally sheet designed for classroom experiments.

It looks like you've uploaded a worksheet titled "Dice Probability" that involves rolling a die and recording the outcomes. The task asks students to:

- Roll a die and keep a tally of each roll.
- Repeat this process for 10, 20, 30, and 40 rolls.
- Record the results in a table with columns for each number of rolls.

Here's how to solve and explain this problem step by step:

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🔹 Objective of the Activity

This is an experimental probability exercise. It helps students understand:
- How outcomes of random events (like dice rolls) behave over time.
- That as the number of trials increases, the experimental probabilities get closer to the theoretical probability.

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🔹 Theoretical Background

A standard six-sided die has faces numbered 1 through 6.

- Theoretical probability of rolling any specific number (e.g., a 3) =
$$
\frac{1}{6} \approx 16.67\%
$$

So, over many rolls, we expect each number to appear roughly the same number of times.

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🔹 How to Complete the Worksheet

#### Step 1: Understand the Table
The table has:
- Rows for each die face: 1, 2, 3, 4, 5, 6.
- Columns for: 10 Rolls, 20 Rolls, 30 Rolls, 40 Rolls.

You will record how many times each number appears after each set of rolls.

For example:
- After 10 rolls: Count how many times you rolled a 1, a 2, etc.
- Then do 10 more rolls (total 20), and count again — now you’ll have cumulative counts.
- Continue up to 40 rolls.

> 💡 Note: The counts should be cumulative, meaning the 20-roll column includes all rolls from the first 10 + next 10, etc.

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🔹 Example of How to Fill It In

Let’s say your rolls go like this:

#### First 10 rolls:
```
4, 2, 6, 1, 3, 5, 2, 1, 6, 3
```

Count:
- 1: 2 times
- 2: 2 times
- 3: 2 times
- 4: 1 time
- 5: 1 time
- 6: 2 times

→ Enter these numbers under 10 Rolls.

#### Next 10 rolls (rolls 11–20):
```
1, 4, 5, 2, 6, 3, 1, 4, 5, 2
```

Add to previous totals:
- 1: 2 + 2 = 4
- 2: 2 + 2 = 4
- 3: 2 + 1 = 3
- 4: 1 + 2 = 3
- 5: 1 + 2 = 3
- 6: 2 + 1 = 3

→ Enter these under 20 Rolls.

Repeat for 30 and 40 rolls.

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🔹 What to Expect

After 40 rolls:
- Each number should appear around $ \frac{40}{6} \approx 6.67 $ times.
- You might see something like:
- 1: 7 times
- 2: 6 times
- 3: 7 times
- 4: 6 times
- 5: 7 times
- 6: 7 times

These are close to equal — showing that the law of large numbers applies: the more rolls, the closer the results match the expected probability.

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🔹 Conclusion & Explanation

This activity demonstrates:
1. Experimental vs. Theoretical Probability
- Theoretical: Each number has a $ \frac{1}{6} $ chance.
- Experimental: Based on actual rolls; may vary early on but stabilizes over time.

2. Randomness and Patterns
- Early on (e.g., 10 rolls), results can be skewed (e.g., one number appears 4 times).
- With more rolls, the distribution evens out.

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✔ Final Tips for Students:

- Use a real die or a random number generator (e.g., online dice roller).
- Keep track of every roll carefully.
- Double-check your tallies.
- Compare your final results to $ \frac{1}{6} $ — did each number appear about equally?

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Would you like me to generate a sample completed table based on simulated dice rolls?