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 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 of 2 = 10/61 ≈ 0.164
Expected probability of 4 = 9/61 ≈ 0.148
Expected probability of 6 = 6/61 ≈ 0.098
Expected probability of 8 = 15/61 ≈ 0.246
Expected probability of 10 = 13/61 ≈ 0.213
Expected probability of 12 = 8/61 ≈ 0.131
Now, we calculate the discrepancies between the experimental and expected probabilities for each outcome:
Discrepancy for 2 = |0.164 - (10/61)| ≈ 0.000
Discrepancy for 4 = |0.148 - (9/61)| ≈ 0.001
Discrepancy for 6 = |0.098 - (6/61)| ≈ 0.001
Discrepancy for 8 = |0.246 - (15/61)| ≈ 0.000
Discrepancy for 10 = |0.213 - (13/61)| ≈ 0.000
Discrepancy for 12 = |0.131 - (8/61)| ≈ 0.001
The smallest discrepancy between the experimental and expected probability is 0.000.
Wrong
I apologize for the mistake. Let's recalculate the discrepancies between the experimental and expected probabilities:
Expected probability of 2 = 10/61 ≈ 0.164
Expected probability of 4 = 9/61 ≈ 0.148
Expected probability of 6 = 6/61 ≈ 0.098
Expected probability of 8 = 15/61 ≈ 0.246
Expected probability of 10 = 13/61 ≈ 0.213
Expected probability of 12 = 8/61 ≈ 0.131
Now, we calculate the discrepancies for each outcome:
Discrepancy for 2 = |0.164 - (10/61)| ≈ 0.000
Discrepancy for 4 = |0.148 - (9/61)| ≈ 0.001
Discrepancy for 6 = |0.098 - (6/61)| ≈ 0.000
Discrepancy for 8 = |0.246 - (15/61)| ≈ 0.000
Discrepancy for 10 = |0.213 - (13/61)| ≈ 0.000
Discrepancy for 12 = |0.131 - (8/61)| ≈ 0.000
The smallest discrepancy between the experimental and expected probability is 0.000. Thank you for your patience.