Use the table to answer the 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. (1 point)

Answer 1

To calculate the expected probability, we divide each frequency by the total number of outcomes:

Total outcomes = 10 + 9 + 6 + 15 + 13 + 8 = 61

Expected probability for each outcome:
2: 10/61 ≈ 0.164
4: 9/61 ≈ 0.148
6: 6/61 ≈ 0.098
8: 15/61 ≈ 0.246
10: 13/61 ≈ 0.213
12: 8/61 ≈ 0.131

Now we can calculate the discrepancy for each outcome by taking the absolute difference between the experimental and expected probabilities:

Discrepancy for 2: |0.164 - 0.164| = 0
Discrepancy for 4: |0.148 - 0.148| = 0
Discrepancy for 6: |0.098 - 0.098| = 0
Discrepancy for 8: |0.246 - 0.246| = 0
Discrepancy for 10: |0.213 - 0.213| = 0
Discrepancy for 12: |0.131 - 0.131| = 0

The smallest discrepancy between the experimental and expected probability is 0, which means that the experiment results match the expected probabilities exactly.