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 largest discrepancy between the experimental and the expected probability of this experiment? The answer needs to be in percent form to the nearest whole number.
Outcomes. 2 4 6 8 10 12
Frequency 10 9 6 15 13 8
To calculate the expected probability for each outcome, we divide the total number of trials (10 + 9 + 6 + 15 + 13 + 8 = 61) by the total number of outcomes (6). This gives us 61/6 = 10.17.
Expected probability for each outcome:
2: 10.17/2 = 5.08
4: 10.17/2 = 5.08
6: 10.17/2 = 5.08
8: 10.17/2 = 5.08
10: 10.17/2 = 5.08
12: 10.17/2 = 5.08
Now, let's calculate the discrepancies between the experimental and expected probabilities for each outcome:
Discrepancy for outcome 2: |10/61 - 5.08| = |0.164 - 5.08| = |-4.916| = 4.92
Discrepancy for outcome 4: |9/61 - 5.08| = |0.148 - 5.08| = |-4.932| = 4.93
Discrepancy for outcome 6: |6/61 - 5.08| = |0.098 - 5.08| = |-4.982| = 4.98
Discrepancy for outcome 8: |15/61 - 5.08| = |0.246 - 5.08| = |-4.834| = 4.83
Discrepancy for outcome 10: |13/61 - 5.08| = |0.213 - 5.08| = |-4.867| = 4.87
Discrepancy for outcome 12: |8/61 - 5.08| = |0.131 - 5.08| = |-4.949| = 4.95
The largest discrepancy is 4.98, which is for outcome 6. Converted to percent form, the largest discrepancy is 498%.