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 your answer in 3 decimal places, rounded to the nearest thousandth.
To find the expected probability, we divide the number of times each outcome appears by the total number of outcomes rolled, which is the sum of all the frequencies:
Expected probability of rolling a 2: 10/61 ≈ 0.164
Expected probability of rolling a 4: 9/61 ≈ 0.148
Expected probability of rolling a 6: 6/61 ≈ 0.098
Expected probability of rolling an 8: 15/61 ≈ 0.246
Expected probability of rolling a 10: 13/61 ≈ 0.213
Expected probability of rolling a 12: 8/61 ≈ 0.131
The experimental probabilities are the frequencies divided by the total number of outcomes, which is 61. Comparing these experimental probabilities to the expected probabilities, we find the smallest discrepancy to be for rolling a 6 with a difference of 0.022.
Therefore, the smallest discrepancy between the experimental and expected probability of this experiment is 0.022.