This educational worksheet compares theoretical probability (what should happen) with experimental probability (what actually happens) using dice and spinner examples.

It looks like you've uploaded an image of a worksheet on theoretical and experimental probability, but the actual image isn't visible in this chat interface. However, based on your description and the text you've provided, I can help explain how to solve typical problems found on such a worksheet.

Let’s go through both Theoretical Probability and Experimental Probability with clear definitions and examples, as well as common questions that appear on such worksheets.

---

🔹 Theoretical Probability

Definition:
> Theoretical probability is what *should* happen based on reasoning, not actual experiments. It's calculated using:

\[
\text{Theoretical Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\]

#### Example:
Suppose you roll a fair 6-sided die.

- What is the theoretical probability of rolling a 4?

\[
P(4) = \frac{1}{6}
\]

Because there is 1 favorable outcome (rolling a 4) out of 6 possible outcomes (1 through 6).

---

#### Common Questions on Theoretical Probability:

1. What is the theoretical probability of landing on A?
- If a spinner has 4 equal sections labeled A, B, C, D:
\[
P(A) = \frac{1}{4}
\]

2. If the spinner is spun 30 times, how many times should we expect it to land on A?
- Expected frequency = Probability × Number of trials
\[
\frac{1}{4} \times 30 = 7.5 \approx 8 \text{ times}
\]
- So, we expect about 8 times.

3. What is the theoretical probability of landing on an odd number?
- If spinning a die: odd numbers are 1, 3, 5 → 3 favorable outcomes
\[
P(\text{odd}) = \frac{3}{6} = \frac{1}{2}
\]

---

🔹 Experimental Probability

Definition:
> Experimental probability is what *actually happens* during an experiment. It's based on observed data.

\[
\text{Experimental Probability} = \frac{\text{Number of times desired outcome occurs}}{\text{Total number of trials}}
\]

#### Example:
You spin a spinner 24 times and record the results:

| Outcome | A | B | C | D |
|--------|---|---|---|---|
| Count | 6 | 5 | 7 | 6 |

- Experimental probability of landing on A:
\[
P(A) = \frac{6}{24} = \frac{1}{4}
\]

- Experimental probability of landing on C:
\[
P(C) = \frac{7}{24}
\]

---

#### Common Questions on Experimental Probability:

1. What is the experimental probability of landing on A?
- Use the table: if A occurred 6 times out of 24 spins → \( \frac{6}{24} = \frac{1}{4} \)

2. What is the experimental probability of landing on an even number?
- Suppose you rolled a die 50 times and got even numbers (2, 4, 6) 25 times.
\[
P(\text{even}) = \frac{25}{50} = \frac{1}{2}
\]

3. How do theoretical and experimental probabilities compare?
- They may be close if the experiment has many trials.
- With few trials, they might differ due to randomness.
- As more trials are done, experimental probability tends to get closer to theoretical probability (this is the Law of Large Numbers).

---

🔹 Key Differences Summary

| Feature | Theoretical Probability | Experimental Probability |
|--------------------------|-------------------------------|----------------------------------|
| Based on | Reasoning / math | Actual data from experiments |
| Formula | Favorable / Total outcomes | Observed / Total trials |
| Changes? | No (for fair conditions) | Yes (varies with trial results) |
| Example | Rolling a 4 on a die: 1/6 | In 60 rolls, 12 were 4s → 12/60 |

---

✔ Final Tip:

On your worksheet, look for:
- Theoretical: "What should happen?" → use fractions based on total possibilities.
- Experimental: "What actually happened?" → use data from tables or charts.

If you can describe the specific problem or give the numbers from the image (like spinner labels or table results), I can walk you through solving it step by step!

Let me know what part you'd like help with!