Someone talks to cube with faces numbered with two, four, six, eight, 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? Please write the answer in three decimal places, rounded to the nearest thousandth. The frequency of two is 10, the frequency of four is 9, the frequency of 6 is 6, the frequency of 8 is 15, the frequency of 10 is 13 and the frequency of 12 is 8

Answer 1

To find the expected probability, we divide the total number of trials by the number of faces on the cube:
Total number of trials = 10 + 9 + 6 + 15 + 13 + 8 = 61
Expected probability = 1/6

Now, let's calculate the observed probability for each face:
- Face 2: 10/61
- Face 4: 9/61
- Face 6: 6/61
- Face 8: 15/61
- Face 10: 13/61
- Face 12: 8/61

Now, let's find the discrepancy for each face:
- Discrepancy for face 2: |10/61 - 1/6| = 0.005
- Discrepancy for face 4: |9/61 - 1/6| = 0.015
- Discrepancy for face 6: |6/61 - 1/6| = 0.003
- Discrepancy for face 8: |15/61 - 1/6| = 0.016
- Discrepancy for face 10: |13/61 - 1/6| = 0.014
- Discrepancy for face 12: |8/61 - 1/6| = 0.008

The smallest discrepancy is 0.003.