Question

Use this 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

wrong

Answer 2

The expected probability for each outcome is 1/6 since there are 6 possible outcomes.

The experimental probability for each outcome is calculated by dividing the frequency by the total number of trials, which is 10 + 9 + 6 + 15 + 13 + 8 = 61.

The discrepancies between the experimental and expected probabilities for each outcome are as follows:
- For outcome 2: |1/6 - 10/61| = 0.033
- For outcome 4: |1/6 - 9/61| = 0.019
- For outcome 6: |1/6 - 6/61| = 0.002
- For outcome 8: |1/6 - 15/61| = 0.079
- For outcome 10: |1/6 - 13/61| = 0.046
- For outcome 12: |1/6 - 8/61| = 0.013

The smallest discrepancy is 0.002, which is between the experimental and expected probabilities for the outcome 6.

Answer 3

I apologize for the mistake. Let's correct it.

The expected probability for each outcome is 1/6 since there are 6 possible outcomes.

The experimental probability for each outcome is calculated by dividing the frequency by the total number of trials, which is 10 + 9 + 6 + 15 + 13 + 8 = 61.

The discrepancies between the experimental and expected probabilities for each outcome are as follows:
- For outcome 2: |1/6 - 10/61| = 0.026
- For outcome 4: |1/6 - 9/61| = 0.009
- For outcome 6: |1/6 - 6/61| = 0.033
- For outcome 8: |1/6 - 15/61| = 0.104
- For outcome 10: |1/6 - 13/61| = 0.076
- For outcome 12: |1/6 - 8/61| = 0.066

The smallest discrepancy is 0.009, which is between the experimental and expected probabilities for the outcome 4.