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 largest discrepancy between the experimental and the expected probability of this experiment? The answer needs to be in percent form to the nearest whole number.
(1 point)
To find the expected probability for each outcome, we calculate the total number of trials first:
Total number of trials = 10 + 9 + 6 + 15 + 13 + 8 = 61
Then we divide the frequency of each outcome by the total number of trials to get the expected probability:
Probability of 2: 10/61 ≈ 0.164
Probability of 4: 9/61 ≈ 0.148
Probability of 6: 6/61 ≈ 0.098
Probability of 8: 15/61 ≈ 0.246
Probability of 10: 13/61 ≈ 0.213
Probability of 12: 8/61 ≈ 0.131
The expected probabilities are:
2: 16.4%
4: 14.8%
6: 9.8%
8: 24.6%
10: 21.3%
12: 13.1%
Now, we compare the experimental probabilities to the expected probabilities to find the largest discrepancy:
Largest discrepancy = |Experimental Probability - Expected Probability|
For outcome 2:
Discrepancy = |(10/61) - 0.164| = |0.164 - 0.164| = 0
For outcome 4:
Discrepancy = |(9/61) - 0.148| = |0.148 - 0.148| = 0
For outcome 6:
Discrepancy = |(6/61) - 0.098| = |0.098 - 0.098| = 0
For outcome 8:
Discrepancy = |(15/61) - 0.246| = |0.246 - 0.246| = 0
For outcome 10:
Discrepancy = |(13/61) - 0.213| = |0.213 - 0.213| = 0
For outcome 12:
Discrepancy = |(8/61) - 0.131| = |0.131 - 0.131| = 0
The largest discrepancy between the experimental and expected probability is 0%, which occurs for all outcomes.
Wrong answer.
Apologies for the mistake. Let's recalculate the largest discrepancy between the experimental and expected probabilities.
The expected probability for each outcome can be calculated by dividing the frequency of each outcome by the total number of trials (61):
Probability of 2: 10/61 ≈ 0.164
Probability of 4: 9/61 ≈ 0.148
Probability of 6: 6/61 ≈ 0.098
Probability of 8: 15/61 ≈ 0.246
Probability of 10: 13/61 ≈ 0.213
Probability of 12: 8/61 ≈ 0.131
Next, we can calculate the experimental probability by dividing the actual frequency of each outcome by the total number of trials:
Experimental Probability of 2: 10/61 ≈ 0.164
Experimental Probability of 4: 9/61 ≈ 0.148
Experimental Probability of 6: 6/61 ≈ 0.098
Experimental Probability of 8: 15/61 ≈ 0.246
Experimental Probability of 10: 13/61 ≈ 0.213
Experimental Probability of 12: 8/61 ≈ 0.131
Now, we can find the discrepancies for each outcome:
Discrepancy for 2: |0.164 - 0.164| = 0
Discrepancy for 4: |0.148 - 0.148| = 0
Discrepancy for 6: |0.098 - 0.098| = 0
Discrepancy for 8: |0.246 - 0.246| = 0
Discrepancy for 10: |0.213 - 0.213| = 0
Discrepancy for 12: |0.131 - 0.131| = 0
Therefore, the largest discrepancy between the experimental and expected probabilities for this experiment is 0%.