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 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)
I apologize for the error in my previous responses. Let's re-calculate the discrepancies for each outcome:
Expected probabilities:
P(2) = 1/6 ≈ 0.167
P(4) = 1/6 ≈ 0.167
P(6) = 1/6 ≈ 0.167
P(8) = 1/6 ≈ 0.167
P(10) = 1/6 ≈ 0.167
P(12) = 1/6 ≈ 0.167
Now, let's find the discrepancies for each outcome:
Discrepancy for 2: |0.164 - 0.167| ≈ 0.003
Discrepancy for 4: |0.148 - 0.167| ≈ 0.019
Discrepancy for 6: |0.098 - 0.167| ≈ 0.069
Discrepancy for 8: |0.246 - 0.167| ≈ 0.079
Discrepancy for 10: |0.213 - 0.167| ≈ 0.046
Discrepancy for 12: |0.131 - 0.167| ≈ 0.036
The smallest discrepancy is 0.003.
To find the expected probability for each outcome, we divide the frequency by the total number of trials:
Total number of trials = 10 + 9 + 6 + 15 + 13 + 8 = 61
Expected probability:
P(2) = 10/61 ≈ 0.164
P(4) = 9/61 ≈ 0.148
P(6) = 6/61 ≈ 0.098
P(8) = 15/61 ≈ 0.246
P(10) = 13/61 ≈ 0.213
P(12) = 8/61 ≈ 0.131
Now we can find the discrepancy for each outcome:
Discrepancy for 2: |P(2) - 1/6| = |0.164 - 1/6| ≈ 0.014
Discrepancy for 4: |P(4) - 1/6| = |0.148 - 1/6| ≈ 0.014
Discrepancy for 6: |P(6) - 1/6| = |0.098 - 1/6| ≈ 0.052
Discrepancy for 8: |P(8) - 1/6| = |0.246 - 1/6| ≈ 0.080
Discrepancy for 10: |P(10) - 1/6| = |0.213 - 1/6| ≈ 0.080
Discrepancy for 12: |P(12) - 1/6| = |0.131 - 1/6| ≈ 0.019
The smallest discrepancy is 0.014.
Wrong
To find the expected probability for each outcome, we divide the frequency by the total number of trials:
Total number of trials = 10 + 9 + 6 + 15 + 13 + 8 = 61
Expected probability:
P(2) = 10/61 ≈ 0.164
P(4) = 9/61 ≈ 0.148
P(6) = 6/61 ≈ 0.098
P(8) = 15/61 ≈ 0.246
P(10) = 13/61 ≈ 0.213
P(12) = 8/61 ≈ 0.131
Now we can find the discrepancy for each outcome:
Discrepancy for 2: |P(2) - 1/6| = |0.164 - 1/6| ≈ 0.014
Discrepancy for 4: |P(4) - 1/6| = |0.148 - 1/6| ≈ 0.015
Discrepancy for 6: |P(6) - 1/6| = |0.098 - 1/6| ≈ 0.053
Discrepancy for 8: |P(8) - 1/6| = |0.246 - 1/6| ≈ 0.080
Discrepancy for 10: |P(10) - 1/6| = |0.213 - 1/6| ≈ 0.080
Discrepancy for 12: |P(12) - 1/6| = |0.131 - 1/6| ≈ 0.019
The smallest discrepancy is 0.014.