Jade tostick you with faces numbered with 246-81012 the results are recorded in the table what is the smallest discrepancy between the experimental and the expected probability of this experiment right your answer in three decimal places rounded to the nearest thousandth
To find the smallest discrepancy between the experimental and expected probability, we need to calculate the expected probability for each face and compare it to the experimental probability.
First, let's calculate the total number of rolls:
Total rolls = 2 + 4 + 6 + 8 + 10 + 12 = 42
Next, we calculate the expected probability for each face:
- Face 2: Expected probability = (1/6) = 0.167
- Face 4: Expected probability = (1/6) = 0.167
- Face 6: Expected probability = (1/6) = 0.167
- Face 8: Expected probability = (1/6) = 0.167
- Face 10: Expected probability = (1/6) = 0.167
- Face 12: Expected probability = (1/6) = 0.167
Now, we calculate the experimental probability for each face from the table:
- Face 2: Experimental probability = 3/42 = 0.071
- Face 4: Experimental probability = 5/42 = 0.119
- Face 6: Experimental probability = 7/42 = 0.167
- Face 8: Experimental probability = 7/42 = 0.167
- Face 10: Experimental probability = 11/42 = 0.262
- Face 12: Experimental probability = 9/42 = 0.214
Next, we calculate the discrepancy between the experimental and expected probability for each face:
- Discrepancy for Face 2: |0.167 - 0.071| = 0.096
- Discrepancy for Face 4: |0.167 - 0.119| = 0.048
- Discrepancy for Face 6: |0.167 - 0.167| = 0
- Discrepancy for Face 8: |0.167 - 0.167| = 0
- Discrepancy for Face 10: |0.167 - 0.262| = 0.095
- Discrepancy for Face 12: |0.167 - 0.214| = 0.047
The smallest discrepancy is 0, as it is the smallest difference between the expected and experimental probabilities.
Therefore, the smallest discrepancy between the experimental and expected probability of this experiment is 0.000, or 0 as rounded to the nearest thousandth.