Question

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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the expected probability for each outcome, we first need to calculate the total number of results, which is the sum of the frequencies:

Total number of results = 10 + 9 + 6 + 15 + 13 + 8 = 61

Then, we calculate the expected probability for each outcome by dividing the frequency by the total number of results:

Expected probability:
2: 10/61 ≈ 0.164
4: 9/61 ≈ 0.148
6: 6/61 ≈ 0.098
8: 15/61 ≈ 0.246
10: 13/61 ≈ 0.213
12: 8/61 ≈ 0.131

Now, we compare the experimental probabilities with the expected probabilities:

Smallest discrepancy:
|0.164 - 0.164| = 0
|0.148 - 0.148| = 0
|0.098 - 0.098| = 0
|0.246 - 0.246| = 0
|0.213 - 0.213| = 0
|0.131 - 0.131| = 0

Therefore, the smallest discrepancy between the experimental and expected probability of this experiment is 0.