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 largest discrepancy between the experimental and the expected probability of this experiment? The answer needs to be in percent form to the nearest whole number. (1 point) %
To find the largest discrepancy between the experimental and expected probability of this experiment, we need to calculate the expected probability for each number and then compare it to the experimental probability.
Expected probability for each number:
- The total number of faces on the cube is 6.
- The expected probability for each number is 1/6.
Therefore, the expected probabilities are:
- 2: 1/6 ≈ 16.67%
- 4: 1/6 ≈ 16.67%
- 6: 1/6 ≈ 16.67%
- 8: 1/6 ≈ 16.67%
- 10: 1/6 ≈ 16.67%
- 12: 1/6 ≈ 16.67%
Experimental probabilities (based on the table provided):
- 2: 2/30 = 2/30 ≈ 6.67%
- 4: 6/30 = 6/30 = 20%
- 6: 4/30 = 4/30 ≈ 13.33%
- 8: 6/30 = 6/30 = 20%
- 10: 7/30 = 7/30 ≈ 23.33%
- 12: 5/30 = 5/30 ≈ 16.67%
Now, we find the largest discrepancy between the experimental and expected probability by comparing all values:
- For number 6: |Experimental Probability - Expected Probability| = |13.33% - 16.67%| ≈ 3.34%
Therefore, the largest discrepancy between the experimental and expected probability of this experiment is approximately 3.34%, rounded to the nearest whole number.