Question

Outcomes 2


468


10 12

Frequency 10 9 6 15 13 8





Use the table to answer the question.
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.

Answer 1

To find the smallest discrepancy between the experimental and expected probability, we need to first calculate the experimental probability and expected probability for each outcome.

Experimental Probability:
- Outcome 2: 10 occurrences out of 61 total trials = 10/61 ≈ 0.164
- Outcome 4: 9 occurrences out of 61 total trials = 9/61 ≈ 0.148
- Outcome 6: 6 occurrences out of 61 total trials = 6/61 ≈ 0.098
- Outcome 8: 15 occurrences out of 61 total trials = 15/61 ≈ 0.246
- Outcome 10: 13 occurrences out of 61 total trials = 13/61 ≈ 0.213
- Outcome 12: 8 occurrences out of 61 total trials = 8/61 ≈ 0.131

Expected Probability:
Since each face has an equal probability of 1/6 = 0.167, we can expect the following probabilities:
- Outcome 2: 0.167
- Outcome 4: 0.167
- Outcome 6: 0.167
- Outcome 8: 0.167
- Outcome 10: 0.167
- Outcome 12: 0.167

Now, we can calculate the discrepancies:
- For Outcome 2: |0.164 - 0.167| = 0.003
- For Outcome 4: |0.148 - 0.167| = 0.019
- For Outcome 6: |0.098 - 0.167| = 0.069
- For Outcome 8: |0.246 - 0.167| = 0.079
- For Outcome 10: |0.213 - 0.167| = 0.046
- For Outcome 12: |0.131 - 0.167| = 0.036

The smallest discrepancy is between Outcome 2 with a discrepancy of 0.003. So, the smallest discrepancy between the experimental and expected probability of this experiment is 0.003.