Question

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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the expected probability for each outcome, we need to divide the frequency of each outcome by the total number of trials. The total number of trials is the sum of all the frequencies, which is 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 need to find the discrepancy between the experimental and expected probability for each outcome. The discrepancy is calculated by taking the absolute difference between the experimental and expected probabilities.

Discrepancy for outcome 2: |0.164 - 0.164| = 0
Discrepancy for outcome 4: |0.148 - 0.148| = 0
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 expected probability is 0.000.