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.
Outcomes: 2, 4, 6, 8, 10, 12
Frequency: 10, 9 , 6, 15, 13, 8
Expected probabilities:
- P(2) = 1/6 ≈ 0.167
- P(4) = 1/6 ≈ 0.167
- P(6) = 1/6 ≈ 0.167
- P(8) = 1/6 ≈ 0.167
- P(10) = 1/6 ≈ 0.167
- P(12) = 1/6 ≈ 0.167
Experimental probabilities:
- P(2) = 10/61 ≈ 0.164
- P(4) = 9/61 ≈ 0.148
- P(6) = 6/61 ≈ 0.098
- P(8) = 15/61 ≈ 0.246
- P(10) = 13/61 ≈ 0.213
- P(12) = 8/61 ≈ 0.131
The discrepancies are as follows:
- For 2: |0.164 - 0.167| = 0.003
- For 4: |0.148 - 0.167| = 0.019
- For 6: |0.098 - 0.167| = 0.069
- For 8: |0.246 - 0.167| = 0.079
- For 10: |0.213 - 0.167| = 0.046
- For 12: |0.131 - 0.167| = 0.036
The smallest discrepancy is 0.003, which is for the outcome 2.