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 find the expected probability of each outcome, we need to divide each frequency 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 can calculate the absolute difference between the experimental and expected probabilities for each outcome:
|0.164 - 0.148| = 0.016
|0.148 - 0.148| = 0
|0.098 - 0.098| = 0
|0.246 - 0.246| = 0
|0.213 - 0.213| = 0
|0.131 - 0.131| = 0
The smallest discrepancy between the experimental and expected probability is 0.016.