To determine the largest discrepancy between the experimental and the expected probability of the outcomes from Jade's experiment, we first need to calculate the experimental probabilities for each outcome and compare them to the expected probabilities.
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Total frequency of outcomes: \[ \text{Total frequency} = 10 + 9 + 6 + 15 + 13 + 8 = 61 \]
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Experimental probabilities for each outcome:
- For 2: \[ P(2) = \frac{10}{61} \approx 0.1639 \]
- For 4: \[ P(4) = \frac{9}{61} \approx 0.1475 \]
- For 6: \[ P(6) = \frac{6}{61} \approx 0.0984 \]
- For 8: \[ P(8) = \frac{15}{61} \approx 0.2459 \]
- For 10: \[ P(10) = \frac{13}{61} \approx 0.2131 \]
- For 12: \[ P(12) = \frac{8}{61} \approx 0.1311 \]
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Expected probabilities for the outcomes of a fair die (assuming each number is equally likely): Since there are 6 outcomes (2, 4, 6, 8, 10, and 12), the expected probability for each outcome is: \[ P(\text{any outcome}) = \frac{1}{6} \approx 0.1667 \]
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Finding the discrepancies: Now we calculate the discrepancies between the experimental probabilities and the expected probabilities:
- For 2: \[ |P(2) - P(\text{expected})| = |0.1639 - 0.1667| \approx 0.0028 \]
- For 4: \[ |P(4) - P(\text{expected})| = |0.1475 - 0.1667| \approx 0.0192 \]
- For 6: \[ |P(6) - P(\text{expected})| = |0.0984 - 0.1667| \approx 0.0683 \]
- For 8: \[ |P(8) - P(\text{expected})| = |0.2459 - 0.1667| \approx 0.0792 \]
- For 10: \[ |P(10) - P(\text{expected})| = |0.2131 - 0.1667| \approx 0.0464 \]
- For 12: \[ |P(12) - P(\text{expected})| = |0.1311 - 0.1667| \approx 0.0356 \]
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Conclusion: The largest discrepancy is for the outcome 8, with a discrepancy of approximately 0.0792.
Thus, the outcome value with the largest discrepancy between the experimental and expected probability is 8.