The expected probability of each outcome when rolling a fair six-sided die is 1/6 or approximately 16.67%.
Calculating the experimental probability for each outcome:
- Outcome 2: 10/61 ≈ 16.39%
- Outcome 4: 9/61 ≈ 14.75%
- Outcome 6: 6/61 ≈ 9.84%
- Outcome 8: 15/61 ≈ 24.59%
- Outcome 10: 13/61 ≈ 21.31%
- Outcome 12: 8/61 ≈ 13.11%
The largest discrepancy between the experimental and expected probability is for outcome 6, which has a difference of |9.84% - 16.67%| ≈ 6.83%.
Therefore, the largest discrepancy between the experimental and expected probability is approximately 7%.
Outcomes 2 4 6 8 10 12
Frequency 10 9 6 15 13 8
Jede tossed a cube with faces numbered with 2, 4, 6, 8, 10, and 12. The results are recorded in the table. What is the largest discrepancy between the experimental and the expected probability of this experiment? The answer needs to be in percent form to the nearest whole number.
(1 point)
%
7 answers
nope wrong
I apologize for the mistake. Let's recalculate the largest discrepancy between the experimental and expected probability.
Given frequencies:
- Outcome 2: 10
- Outcome 4: 9
- Outcome 6: 6
- Outcome 8: 15
- Outcome 10: 13
- Outcome 12: 8
Expected frequency for each outcome on a fair die: 61/6 = 10.17
Calculating the discrepancy for each outcome:
- Outcome 2: |10 - 10.17| = 0.17
- Outcome 4: |9 - 10.17| = 1.17
- Outcome 6: |6 - 10.17| = 4.17
- Outcome 8: |15 - 10.17| = 4.83
- Outcome 10: |13 - 10.17| = 2.83
- Outcome 12: |8 - 10.17| = 2.17
The largest discrepancy is 4.83, which occurs for outcome 8.
Expressing this discrepancy as a percentage of the expected frequency:
(4.83/10.17) * 100 ≈ 47%
Therefore, the largest discrepancy between the experimental and expected probability is approximately 47%.
Given frequencies:
- Outcome 2: 10
- Outcome 4: 9
- Outcome 6: 6
- Outcome 8: 15
- Outcome 10: 13
- Outcome 12: 8
Expected frequency for each outcome on a fair die: 61/6 = 10.17
Calculating the discrepancy for each outcome:
- Outcome 2: |10 - 10.17| = 0.17
- Outcome 4: |9 - 10.17| = 1.17
- Outcome 6: |6 - 10.17| = 4.17
- Outcome 8: |15 - 10.17| = 4.83
- Outcome 10: |13 - 10.17| = 2.83
- Outcome 12: |8 - 10.17| = 2.17
The largest discrepancy is 4.83, which occurs for outcome 8.
Expressing this discrepancy as a percentage of the expected frequency:
(4.83/10.17) * 100 ≈ 47%
Therefore, the largest discrepancy between the experimental and expected probability is approximately 47%.
no
Apologies for the mistakes. Let's recalculate the largest discrepancy between the experimental and expected probability.
Given frequencies:
- Outcome 2: 10
- Outcome 4: 9
- Outcome 6: 6
- Outcome 8: 15
- Outcome 10: 13
- Outcome 12: 8
Total frequency: 10 + 9 + 6 + 15 + 13 + 8 = 61
Expected probability of each outcome on a fair die: 1/6 or approximately 16.67%
Expected frequency for each outcome on a fair die: 61 * 1/6 ≈ 10.17
Calculating the discrepancy for each outcome:
- Outcome 2: |10 - 10.17| = 0.17
- Outcome 4: |9 - 10.17| = 1.17
- Outcome 6: |6 - 10.17| = 4.17
- Outcome 8: |15 - 10.17| = 4.83
- Outcome 10: |13 - 10.17| = 2.83
- Outcome 12: |8 - 10.17| = 2.17
The largest discrepancy is 4.83, which occurs for outcome 8.
Expressing this discrepancy as a percentage of the expected frequency:
(4.83/10.17) * 100 ≈ 47.43%
Therefore, the largest discrepancy between the experimental and expected probability is approximately 47.43%.
Given frequencies:
- Outcome 2: 10
- Outcome 4: 9
- Outcome 6: 6
- Outcome 8: 15
- Outcome 10: 13
- Outcome 12: 8
Total frequency: 10 + 9 + 6 + 15 + 13 + 8 = 61
Expected probability of each outcome on a fair die: 1/6 or approximately 16.67%
Expected frequency for each outcome on a fair die: 61 * 1/6 ≈ 10.17
Calculating the discrepancy for each outcome:
- Outcome 2: |10 - 10.17| = 0.17
- Outcome 4: |9 - 10.17| = 1.17
- Outcome 6: |6 - 10.17| = 4.17
- Outcome 8: |15 - 10.17| = 4.83
- Outcome 10: |13 - 10.17| = 2.83
- Outcome 12: |8 - 10.17| = 2.17
The largest discrepancy is 4.83, which occurs for outcome 8.
Expressing this discrepancy as a percentage of the expected frequency:
(4.83/10.17) * 100 ≈ 47.43%
Therefore, the largest discrepancy between the experimental and expected probability is approximately 47.43%.
and no
I apologize for the errors in the previous calculations. Let's correct the calculation for the largest discrepancy between the experimental and expected probability.
Given frequencies:
- Outcome 2: 10
- Outcome 4: 9
- Outcome 6: 6
- Outcome 8: 15
- Outcome 10: 13
- Outcome 12: 8
Total frequency: 61 (sum of all frequencies)
Expected probability of each outcome on a fair die: 1/6 or approximately 16.67%
Expected frequency for each outcome on a fair die: 61 * 1/6 ≈ 10.17
Calculating the discrepancy for each outcome:
- Outcome 2: |10 - 10.17| = 0.17
- Outcome 4: |9 - 10.17| = 1.17
- Outcome 6: |6 - 10.17| = 4.17
- Outcome 8: |15 - 10.17| = 4.83
- Outcome 10: |13 - 10.17| = 2.83
- Outcome 12: |8 - 10.17| = 2.17
The largest discrepancy is 4.83, which occurs for outcome 8.
Expressing this discrepancy as a percentage of the expected frequency:
(4.83/10.17) * 100 ≈ 47.5%
Therefore, the largest discrepancy between the experimental and expected probability is approximately 47.5%. Thank you for your patience.
Given frequencies:
- Outcome 2: 10
- Outcome 4: 9
- Outcome 6: 6
- Outcome 8: 15
- Outcome 10: 13
- Outcome 12: 8
Total frequency: 61 (sum of all frequencies)
Expected probability of each outcome on a fair die: 1/6 or approximately 16.67%
Expected frequency for each outcome on a fair die: 61 * 1/6 ≈ 10.17
Calculating the discrepancy for each outcome:
- Outcome 2: |10 - 10.17| = 0.17
- Outcome 4: |9 - 10.17| = 1.17
- Outcome 6: |6 - 10.17| = 4.17
- Outcome 8: |15 - 10.17| = 4.83
- Outcome 10: |13 - 10.17| = 2.83
- Outcome 12: |8 - 10.17| = 2.17
The largest discrepancy is 4.83, which occurs for outcome 8.
Expressing this discrepancy as a percentage of the expected frequency:
(4.83/10.17) * 100 ≈ 47.5%
Therefore, the largest discrepancy between the experimental and expected probability is approximately 47.5%. Thank you for your patience.
1 answer