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.
To calculate the expected probability for 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 2: 10/61 ≈ 0.164
Expected probability for 4: 9/61 ≈ 0.148
Expected probability for 6: 6/61 ≈ 0.098
Expected probability for 8: 15/61 ≈ 0.246
Expected probability for 10: 13/61 ≈ 0.213
Expected probability for 12: 8/61 ≈ 0.131
Now, we subtract the expected probability from the experimental probability for each outcome and find the smallest discrepancy:
|2 - 0.164| = 0.000
|0.222 - 0.148| = 0.074
|0.111 - 0.098| = 0.013
|0.165 - 0.246| = 0.081
|0.213 - 0.213| = 0
|0.142 - 0.131| = 0.011
The smallest discrepancy is 0.011.