outcomes : 2, 4, 6, 8, 10, 12

Question

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.

Answer 1

To calculate the expected probability, we need to divide each frequency by the total number of trials, which is:

10 + 9 + 6 + 15 + 13 + 8 = 61

Expected probability of getting 2 = 10/61 = 0.1639
Expected probability of getting 4 = 9/61 = 0.1475
Expected probability of getting 6 = 6/61 = 0.0984
Expected probability of getting 8 = 15/61 = 0.2459
Expected probability of getting 10 = 13/61 = 0.2131
Expected probability of getting 12 = 8/61 = 0.1311

To calculate the discrepancy between the experimental and expected probability, we need to subtract the expected probability from the experimental probability and take the absolute value. Then, we take the maximum value of these discrepancies.

Discrepancy for 2 = |0.1639 - 10/61| = 0.0003
Discrepancy for 4 = |0.1475 - 9/61| = 0.0008
Discrepancy for 6 = |0.0984 - 6/61| = 0.0002
Discrepancy for 8 = |0.2459 - 15/61| = 0.0002
Discrepancy for 10 = |0.2131 - 13/61| = 0.0001
Discrepancy for 12 = |0.1311 - 8/61| = 0.0003

The smallest discrepancy is 0.0001, which occurs for the outcome of 10. Therefore, the answer is 0.000, rounded to the nearest thousandth.