To determine which outcome value has the largest discrepancy between the experimental and expected probabilities, we first calculate the experimental probabilities based on the given frequencies.
The total number of tosses can be calculated by summing up the frequencies:
Total frequency = 10 + 9 + 6 + 15 + 13 + 8 = 61
Now, we can calculate the experimental probability for each outcome:
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For outcome 2:
- Experimental Probability = Frequency / Total = 10 / 61 ≈ 0.1639
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For outcome 4:
- Experimental Probability = Frequency / Total = 9 / 61 ≈ 0.1475
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For outcome 6:
- Experimental Probability = Frequency / Total = 6 / 61 ≈ 0.0984
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For outcome 8:
- Experimental Probability = Frequency / Total = 15 / 61 ≈ 0.2459
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For outcome 10:
- Experimental Probability = Frequency / Total = 13 / 61 ≈ 0.2131
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For outcome 12:
- Experimental Probability = Frequency / Total = 8 / 61 ≈ 0.1311
Next, we verify the expected probabilities. Since the cube has six distinct outcomes (2, 4, 6, 8, 10, and 12), and assuming a fair cube, each outcome is equally likely. Thus, the expected probability for each outcome is:
Expected Probability = 1 / 6 ≈ 0.1667
Now, we will calculate the discrepancies between the experimental and expected probabilities for each outcome:
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For outcome 2:
- Discrepancy = |0.1639 - 0.1667| ≈ 0.0028
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For outcome 4:
- Discrepancy = |0.1475 - 0.1667| ≈ 0.0192
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For outcome 6:
- Discrepancy = |0.0984 - 0.1667| ≈ 0.0683
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For outcome 8:
- Discrepancy = |0.2459 - 0.1667| ≈ 0.0792
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For outcome 10:
- Discrepancy = |0.2131 - 0.1667| ≈ 0.0464
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For outcome 12:
- Discrepancy = |0.1311 - 0.1667| ≈ 0.0356
Now, let's find the largest discrepancy:
- Discrepancy for outcome 8 has the largest value of 0.0792.
Therefore, the outcome value with the largest discrepancy between the experimental and expected probability is 8.