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 experimental probability for each face of the cube, we divide the number of times each face appeared by the total number of trials (36):
- Face 2 appeared 5 times, so the experimental probability is 5/36 ≈ 0.139
- Face 4 appeared 6 times, so the experimental probability is 6/36 = 0.167
- Face 6 appeared 7 times, so the experimental probability is 7/36 ≈ 0.194
- Face 8 appeared 6 times, so the experimental probability is 6/36 = 0.167
- Face 10 appeared 6 times, so the experimental probability is 6/36 = 0.167
- Face 12 appeared 6 times, so the experimental probability is 6/36 = 0.167
The expected probability for each face is 1/6 ≈ 0.167, as each face has an equal chance of showing up when rolling a fair six-sided die.
The discrepancies between the experimental and expected probability for each face are:
- Face 2: |0.139 - 0.167| = 0.028
- Face 4: |0.167 - 0.167| = 0
- Face 6: |0.194 - 0.167| = 0.027
- Face 8: |0.167 - 0.167| = 0
- Face 10: |0.167 - 0.167| = 0
- Face 12: |0.167 - 0.167| = 0
The smallest discrepancy is 0, which occurs for faces 4, 8, 10, and 12. So, the smallest discrepancy between the experimental and expected probability of this experiment is 0.000.