To find the largest discrepancy between the experimental and expected probability in Angela's experiment with a queue of numbered faces (2, 4, 6, 8, 10, 12), we first need to compute both the expected probability and the experimental frequency.
- Determine expected probabilities:
Since there are six faces, each outcome is assumed to have an equal probability:
- Probability of rolling a 2: \( \frac{1}{6} \)
- Probability of rolling a 4: \( \frac{1}{6} \)
- Probability of rolling a 6: \( \frac{1}{6} \)
- Probability of rolling an 8: \( \frac{1}{6} \)
- Probability of rolling a 10: \( \frac{1}{6} \)
- Probability of rolling a 12: \( \frac{1}{6} \)
- Record the experimental frequencies:
From your provided data:
- Result frequencies:
- 2: 10
- 4: 9
- 6: 15
- 8: 13
- 10: 8
- 12: (not provided, but inferred)
Calculate the total number of trials: \[ 10 + 9 + 15 + 13 + 8 + (number\ of\ 12\ faced) = N \] Assuming you are referring to the drawn outcomes, let’s denote the frequency of 12 as \( x \).
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Total number of outcomes: If combined frequencies sum to a specific number, we know: \[ N = 10 + 9 + 15 + 13 + 8 + x \] If \( x \) is not provided, we cannot determine this sum altogether. But with your message, we can comprehend that 12 is missing, so let's sum up the known frequencies: \[ N = 10 + 9 + 15 + 13 + 8 = 55 + x \]
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Calculate the expected counts: Expected counts for each number based on \( N \): \[ \text{Expected count for each number} = N \times \frac{1}{6} \]
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Discrepancy calculation for each outcome: Discrepancy is calculated as: \[ | \text{Experimental Probability} - \text{Expected Probability} | \]
Calculating discrepancies with experimental frequencies:
- For 2: \[ \text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 10 \]
- For 4: \[ \text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 9 \]
- For 6: \[ \text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 15 \]
- For 8: \[ \text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 13 \]
- For 10: \[ \text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = 8 \]
- For 12: \[ \text{Expected count} = \frac{N}{6}, \quad \text{Experimental} = x \]
Finally, calculate for:
- 2: Discrepancy = \( | 10 - \frac{N}{6} | \)
- 4: Discrepancy = \( | 9 - \frac{N}{6} | \)
- 6: Discrepancy = \( | 15 - \frac{N}{6} | \)
- 8: Discrepancy = \( | 13 - \frac{N}{6} | \)
- 10: Discrepancy = \( | 8 - \frac{N}{6} | \)
- 12: Discrepancy = \( | x - \frac{N}{6} | \)
Considering you seem to need the final answer in whole numbers based on integer results rounded; these discrepancies would need rounding appropriately.
Conclusion: Without the specific frequency of the face numbered 12, you can assess these discrepancies by substituting the value of x and positing all counts directly through initial calculated values. Please clarify this detail or extract the highest based on common intuitive rounding.
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