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Use the table to answer the question. The table presents the frequency of occurrences for numbers 2, 4, 6, 8, and 10 when Jade tossed a cube. 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. (1 point) Remaining Attempts : 3 Skip to navigation

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To determine the smallest discrepancy between the experimental and expected probabilities based on Jade's experiment, we need to follow these steps:

  1. Calculate the Total Number of Tosses: Add up the frequencies of each outcome: \[ 10 + 9 + 6 + 15 + 13 + 8 = 61 \]

  2. Calculate the Expected Probability for Each Outcome: For a fair die with the numbers 2, 4, 6, 8, 10, and 12, the expected probability for each outcome is: \[ P_{\text{expected}} = \frac{1}{6} \quad \text{(since there are 6 outcomes)} \]

  3. Calculate the Experimental Probability for Each Outcome: The experimental probability for each outcome is given by the frequency of each outcome divided by the total number of tosses (61): \[ P_{\text{experimental}}(2) = \frac{10}{61} \approx 0.164 \] \[ P_{\text{experimental}}(4) = \frac{9}{61} \approx 0.148 \] \[ P_{\text{experimental}}(6) = \frac{6}{61} \approx 0.098 \] \[ P_{\text{experimental}}(8) = \frac{15}{61} \approx 0.246 \] \[ P_{\text{experimental}}(10) = \frac{13}{61} \approx 0.213 \] \[ P_{\text{experimental}}(12) = \frac{8}{61} \approx 0.131 \]

  4. Calculate the Discrepancy for Each Outcome: The discrepancy is calculated as the absolute difference between the experimental probability and expected probability: \[ \text{Discrepancy for } 2: \left| \frac{10}{61} - \frac{1}{6} \right| \approx \left| 0.164 - 0.167 \right| \approx 0.003 \] \[ \text{Discrepancy for } 4: \left| \frac{9}{61} - \frac{1}{6} \right| \approx \left| 0.148 - 0.167 \right| \approx 0.019 \] \[ \text{Discrepancy for } 6: \left| \frac{6}{61} - \frac{1}{6} \right| \approx \left| 0.098 - 0.167 \right| \approx 0.069 \] \[ \text{Discrepancy for } 8: \left| \frac{15}{61} - \frac{1}{6} \right| \approx \left| 0.246 - 0.167 \right| \approx 0.079 \] \[ \text{Discrepancy for } 10: \left| \frac{13}{61} - \frac{1}{6} \right| \approx \left| 0.213 - 0.167 \right| \approx 0.046 \] \[ \text{Discrepancy for } 12: \left| \frac{8}{61} - \frac{1}{6} \right| \approx \left| 0.131 - 0.167 \right| \approx 0.036 \]

  5. Find the Smallest Discrepancy: The smallest discrepancy found is for the outcome of 2, which is approximately 0.003.

Thus, the smallest discrepancy between the experimental and expected probability of this experiment is \(\boxed{0.003}\).