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 smallest discrepancy between the experimental and the expected probability of this experiment?
Write your answer in 3 decimal places, rounded to the nearest thousandth.
To find the expected probability for each outcome, we need to divide the frequency of each outcome by the total number of trials:
Total number of trials = 10 + 9 + 6 + 15 + 13 + 8 = 61
Expected probability for outcome 2 = 10/61 ≈ 0.164
Expected probability for outcome 4 = 9/61 ≈ 0.148
Expected probability for outcome 6 = 6/61 ≈ 0.098
Expected probability for outcome 8 = 15/61 ≈ 0.246
Expected probability for outcome 10 = 13/61 ≈ 0.213
Expected probability for outcome 12 = 8/61 ≈ 0.131
Now, we can find the discrepancy for each outcome:
Discrepancy for outcome 2 = |0.164 - 0.167| = 0.003
Discrepancy for outcome 4 = |0.148 - 0.167| = 0.019
Discrepancy for outcome 6 = |0.098 - 0.167| = 0.069
Discrepancy for outcome 8 = |0.246 - 0.167| = 0.079
Discrepancy for outcome 10 = |0.213 - 0.167| = 0.046
Discrepancy for outcome 12 = |0.131 - 0.167| = 0.036
The smallest discrepancy is 0.003.
Therefore, the smallest discrepancy between the experimental and the expected probability of this experiment is 0.003.
wrong
My apologies for the error in my previous calculation. Let's correct it.
The expected probability for each outcome is as follows:
Outcome 2: 1/6 = 0.167
Outcome 4: 1/6 = 0.167
Outcome 6: 1/6 = 0.167
Outcome 8: 1/6 = 0.167
Outcome 10: 1/6 = 0.167
Outcome 12: 1/6 = 0.167
The discrepancies for each outcome are:
Outcome 2: |0.167 - 0.164| = 0.003
Outcome 4: |0.167 - 0.148| = 0.019
Outcome 6: |0.167 - 0.098| = 0.069
Outcome 8: |0.167 - 0.246| = 0.079
Outcome 10: |0.167 - 0.213| = 0.046
Outcome 12: |0.167 - 0.131| = 0.036
The smallest discrepancy is 0.003.
Therefore, the smallest discrepancy between the experimental and the expected probability in this experiment is 0.003, rounded to three decimal places.