To determine the expected probability, we need to calculate the probability of each outcome based on a fair die:
Outcome: 2. Probability: 1/6
Outcome: 4. Probability: 1/6
Outcome: 6. Probability: 1/6
Outcome: 8. Probability: 1/6
Outcome: 10. Probability: 1/6
Outcome: 12. Probability: 1/6
The expected frequency of each outcome can be calculated by multiplying the probability of each outcome by the total number of trials (in this case, the sum of the frequencies):
Expected frequency of outcome 2: (1/6) x 61 ≈ 10.17
Expected frequency of outcome 4: (1/6) x 61 ≈ 10.17
Expected frequency of outcome 6: (1/6) x 61 ≈ 10.17
Expected frequency of outcome 8: (1/6) x 61 ≈ 10.17
Expected frequency of outcome 10: (1/6) x 61 ≈ 10.17
Expected frequency of outcome 12: (1/6) x 61 ≈ 10.17
To find the largest discrepancy between the experiment and the expected probability, we need to compare the actual frequency of each outcome to its expected frequency. The largest discrepancy will occur for the outcome with the largest absolute difference between its actual frequency and expected frequency.
Outcome 2: Actual frequency = 10, expected frequency ≈ 10.17, absolute difference = 0.17
Outcome 4: Actual frequency = 9, expected frequency ≈ 10.17, absolute difference = 1.17
Outcome 6: Actual frequency = 6, expected frequency ≈ 10.17, absolute difference = 4.17
Outcome 8: Actual frequency = 15, expected frequency ≈ 10.17, absolute difference = 4.83
Outcome 10: Actual frequency = 13, expected frequency ≈ 10.17, absolute difference = 2.83
Outcome 12: Actual frequency = 8, expected frequency ≈ 10.17, absolute difference = 2.17
The largest discrepancy is 4.83, which occurs for outcome 8. Therefore, the largest discrepancy between the experiment and the expected probability of this experiment is 4.83.
Outcomes 2. 4. 6. 8. 10. 12
Frequency 10 9. 6. 15. 13. 8
What is the largest discrepancy between the experiment and the expected probability of this experiment?
1 answer