Question
Angela tossed the queue with faces numbered with 246 810 and 12 the results are recorded in a table. What is the largest discrepancy between the experimental and the expected probability of this experiment? The outcomes is two 468-1012 frequency is 10 96 1513 and eight answer and present form to the nearest whole number
Answers
GPT-4o mini
To find the largest discrepancy between the experimental and expected probability in Angela's experiment with a queue of numbered faces (2, 4, 6, 8, 10, 12), we first need to compute both the expected probability and the experimental frequency.
1. **Determine expected probabilities:**
Since there are six faces, each outcome is assumed to have an equal probability:
- Probability of rolling a 2: \( \frac{1}{6} \)
- Probability of rolling a 4: \( \frac{1}{6} \)
- Probability of rolling a 6: \( \frac{1}{6} \)
- Probability of rolling an 8: \( \frac{1}{6} \)
- Probability of rolling a 10: \( \frac{1}{6} \)
- Probability of rolling a 12: \( \frac{1}{6} \)
2. **Record the experimental frequencies:**
From your provided data:
- Result frequencies:
- 2: 10
- 4: 9
- 6: 15
- 8: 13
- 10: 8
- 12: (not provided, but inferred)
Calculate the total number of trials:
\[
10 + 9 + 15 + 13 + 8 + (number\ of\ 12\ faced) = N
\]
Assuming you are referring to the drawn outcomes, let’s denote the frequency of 12 as \( x \).
3. **Total number of outcomes:**
If combined frequencies sum to a specific number, we know:
\[
N = 10 + 9 + 15 + 13 + 8 + x
\]
If \( x \) is not provided, we cannot determine this sum altogether. But with your message, we can comprehend that 12 is missing, so let's sum up the known frequencies:
\[
N = 10 + 9 + 15 + 13 + 8 = 55 + x
\]
4. **Calculate the expected counts:**
Expected counts for each number based on \( N \):
\[
\text{Expected count for each number} = N \times \frac{1}{6}
\]
5. **Discrepancy calculation for each outcome:**
Discrepancy is calculated as:
\[
| \text{Experimental Probability} - \text{Expected Probability} |
\]
**Calculating discrepancies with experimental frequencies:**
- For 2:
\[
\text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 10
\]
- For 4:
\[
\text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 9
\]
- For 6:
\[
\text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 15
\]
- For 8:
\[
\text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 13
\]
- For 10:
\[
\text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 8
\]
- For 12:
\[
\text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = x
\]
Finally, calculate for:
1. 2: Discrepancy = \( | 10 - \frac{N}{6} | \)
2. 4: Discrepancy = \( | 9 - \frac{N}{6} | \)
3. 6: Discrepancy = \( | 15 - \frac{N}{6} | \)
4. 8: Discrepancy = \( | 13 - \frac{N}{6} | \)
5. 10: Discrepancy = \( | 8 - \frac{N}{6} | \)
6. 12: Discrepancy = \( | x - \frac{N}{6} | \)
Considering you seem to need the final answer in whole numbers based on integer results rounded; these discrepancies would need rounding appropriately.
**Conclusion:** Without the specific frequency of the face numbered 12, you can assess these discrepancies by substituting the value of x and positing all counts directly through initial calculated values. Please clarify this detail or extract the highest based on common intuitive rounding.
1. **Determine expected probabilities:**
Since there are six faces, each outcome is assumed to have an equal probability:
- Probability of rolling a 2: \( \frac{1}{6} \)
- Probability of rolling a 4: \( \frac{1}{6} \)
- Probability of rolling a 6: \( \frac{1}{6} \)
- Probability of rolling an 8: \( \frac{1}{6} \)
- Probability of rolling a 10: \( \frac{1}{6} \)
- Probability of rolling a 12: \( \frac{1}{6} \)
2. **Record the experimental frequencies:**
From your provided data:
- Result frequencies:
- 2: 10
- 4: 9
- 6: 15
- 8: 13
- 10: 8
- 12: (not provided, but inferred)
Calculate the total number of trials:
\[
10 + 9 + 15 + 13 + 8 + (number\ of\ 12\ faced) = N
\]
Assuming you are referring to the drawn outcomes, let’s denote the frequency of 12 as \( x \).
3. **Total number of outcomes:**
If combined frequencies sum to a specific number, we know:
\[
N = 10 + 9 + 15 + 13 + 8 + x
\]
If \( x \) is not provided, we cannot determine this sum altogether. But with your message, we can comprehend that 12 is missing, so let's sum up the known frequencies:
\[
N = 10 + 9 + 15 + 13 + 8 = 55 + x
\]
4. **Calculate the expected counts:**
Expected counts for each number based on \( N \):
\[
\text{Expected count for each number} = N \times \frac{1}{6}
\]
5. **Discrepancy calculation for each outcome:**
Discrepancy is calculated as:
\[
| \text{Experimental Probability} - \text{Expected Probability} |
\]
**Calculating discrepancies with experimental frequencies:**
- For 2:
\[
\text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 10
\]
- For 4:
\[
\text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 9
\]
- For 6:
\[
\text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 15
\]
- For 8:
\[
\text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 13
\]
- For 10:
\[
\text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 8
\]
- For 12:
\[
\text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = x
\]
Finally, calculate for:
1. 2: Discrepancy = \( | 10 - \frac{N}{6} | \)
2. 4: Discrepancy = \( | 9 - \frac{N}{6} | \)
3. 6: Discrepancy = \( | 15 - \frac{N}{6} | \)
4. 8: Discrepancy = \( | 13 - \frac{N}{6} | \)
5. 10: Discrepancy = \( | 8 - \frac{N}{6} | \)
6. 12: Discrepancy = \( | x - \frac{N}{6} | \)
Considering you seem to need the final answer in whole numbers based on integer results rounded; these discrepancies would need rounding appropriately.
**Conclusion:** Without the specific frequency of the face numbered 12, you can assess these discrepancies by substituting the value of x and positing all counts directly through initial calculated values. Please clarify this detail or extract the highest based on common intuitive rounding.