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.
Apologies for the error in my previous response. Let's recalculate the discrepancies between the experimental and expected probabilities and find the smallest one.
Expected probability for outcome 2: 1/6 = 0.167
Expected probability for outcome 4: 1/6 = 0.167
Expected probability for outcome 6: 1/6 = 0.167
Expected probability for outcome 8: 1/6 = 0.167
Expected probability for outcome 10: 1/6 = 0.167
Expected probability for outcome 12: 1/6 = 0.167
Now we can calculate the discrepancy between experimental and expected probabilities 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 between the experimental and the expected probability of this experiment is 0.003.
To find the expected probability of each outcome, we 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 calculate the discrepancy between experimental and expected probabilities for each outcome:
Discrepancy for outcome 2: |0.164 - 0.164| = 0
Discrepancy for outcome 4: |0.149 - 0.148| = 0.001
Discrepancy for outcome 6: |0.098 - 0.098| = 0
Discrepancy for outcome 8: |0.246 - 0.246| = 0
Discrepancy for outcome 10: |0.213 - 0.213| = 0
Discrepancy for outcome 12: |0.131 - 0.131| = 0
The smallest discrepancy between the experimental and the expected probability of this experiment is 0.001.