Question

Roll a dice 20 times

Log your findings in Table Like the one Below:


Answer the following Questions:

According to your Findings, What is the Probability of Rolling a 6? 6/20

According to your Findings, What is the Probability of Rolling a 5? 1/20

According to your Findings, What is the Probability of Rolling a 4?
4/20

According to your Findings, What is the Probability of Rolling a 3?
1/20

According to your Findings, What is the Probability of Rolling a 2? 6/10

According to your Findings, What is the Probability of Rolling a 1? 2/20

If you had two dice, do you think your odds of rolling a 6 would be better or worse? Explain your reasoning. I think it would make it better as I would have double the chances to roll a six

Answer 1

Let's create a hypothetical log for rolling a die 20 times, as it seems you would like to simulate this process. Then, I'll provide answers to your questions based on the findings.

### Dice Roll Results Log

| Roll Number | Result |
|-------------|--------|
| 1 | 3 |
| 2 | 5 |
| 3 | 2 |
| 4 | 6 |
| 5 | 1 |
| 6 | 4 |
| 7 | 6 |
| 8 | 2 |
| 9 | 6 |
| 10 | 2 |
| 11 | 4 |
| 12 | 3 |
| 13 | 5 |
| 14 | 1 |
| 15 | 2 |
| 16 | 3 |
| 17 | 6 |
| 18 | 4 |
| 19 | 5 |
| 20 | 1 |

### Summary of Results

- **1:** 3 times
- **2:** 4 times
- **3:** 3 times
- **4:** 3 times
- **5:** 3 times
- **6:** 5 times

### Findings

- Total Rolls = 20
- Count of Rolling a 6 = 5
- Count of Rolling a 5 = 3
- Count of Rolling a 4 = 3
- Count of Rolling a 3 = 3
- Count of Rolling a 2 = 4
- Count of Rolling a 1 = 3

### Probabilities Based on Findings

- **Probability of Rolling a 6:** \( \frac{5}{20} = \frac{1}{4} \)
- **Probability of Rolling a 5:** \( \frac{3}{20} \)
- **Probability of Rolling a 4:** \( \frac{3}{20} \)
- **Probability of Rolling a 3:** \( \frac{3}{20} \)
- **Probability of Rolling a 2:** \( \frac{4}{20} = \frac{1}{5} \)
- **Probability of Rolling a 1:** \( \frac{3}{20} \)

### Answering the Questions

1. **According to your Findings, What is the Probability of Rolling a 6?**
- **Answer:** \( \frac{5}{20} = \frac{1}{4} \)

2. **According to your Findings, What is the Probability of Rolling a 5?**
- **Answer:** \( \frac{3}{20} \)

3. **According to your Findings, What is the Probability of Rolling a 4?**
- **Answer:** \( \frac{3}{20} \)

4. **According to your Findings, What is the Probability of Rolling a 3?**
- **Answer:** \( \frac{3}{20} \)

5. **According to your Findings, What is the Probability of Rolling a 2?**
- **Answer:** \( \frac{4}{20} = \frac{1}{5} \)

6. **According to your Findings, What is the Probability of Rolling a 1?**
- **Answer:** \( \frac{3}{20} \)

7. **If you had two dice, do you think your odds of rolling a 6 would be better or worse? Explain your reasoning.**
- **Answer:** I think it would be better because when rolling two dice, you can achieve a sum of 6 in multiple ways (1+5, 2+4, 3+3, 4+2, 5+1). Additionally, you also have the chance to roll a 6 on each die individually, giving you more opportunities overall to roll a 6. Each individual die still has a 1/6 chance of rolling a 6.

If you would like to see a different outcome based on more rolls or simulate a new scenario, let me know!