Use the table to answer the question. Outcomes 2 4 6 8 10 12 Frequency 10 9 6 15 13 8 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
The expected probability for each outcome is 1/6 since there are 6 faces on the cube.
The experimental probability for each outcome is calculated by dividing the frequency of that outcome by the total number of trials, which is 10 + 9 + 6 + 15 + 13 + 8 = 61.
So, the experimental probabilities are:
Outcome 2: 10/61
Outcome 4: 9/61
Outcome 6: 6/61
Outcome 8: 15/61
Outcome 10: 13/61
Outcome 12: 8/61
The discrepancies between the experimental and expected probabilities are:
Outcome 2: |1/6 - 10/61| = |1/6 - 0.164| ≈ 0.036
Outcome 4: |1/6 - 9/61| = |1/6 - 0.148| ≈ 0.018
Outcome 6: |1/6 - 6/61| = |1/6 - 0.098| ≈ 0.032
Outcome 8: |1/6 - 15/61| = |1/6 - 0.246| ≈ 0.079
Outcome 10: |1/6 - 13/61| = |1/6 - 0.213| ≈ 0.087
Outcome 12: |1/6 - 8/61| = |1/6 - 0.131| ≈ 0.025
The smallest discrepancy is 0.018 for Outcome 4.