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 largest discrepancy between the experimental and the expected probability of this experiment?
Write your answer in 3 decimal places, rounded to the nearest thousandth.
In this experiment, the expected probability of each outcome is 1/6 since there are 6 possible outcomes on the cube.
To calculate the experimental probability for each outcome, we divide the frequency by the total number of trials:
Experimental probability = Frequency/Total number of trials
Total number of trials = 10 + 9 + 6 + 15 + 13 + 8 = 61
For outcomes 2, 4, 6, 8, 10, 12:
Experimental probability of 2 = 10/61 ≈ 0.164
Experimental probability of 4 = 9/61 ≈ 0.148
Experimental probability of 6 = 6/61 ≈ 0.098
Experimental probability of 8 = 15/61 ≈ 0.246
Experimental probability of 10 = 13/61 ≈ 0.213
Experimental probability of 12 = 8/61 ≈ 0.131
Now, we find the largest discrepancy between the experimental and expected probability:
|Experimental probability - Expected probability|:
|0.164 - 1/6| = 0.164 - 0.167 ≈ 0.003 (for outcome 2)
|0.148 - 1/6| = 0.148 - 0.167 ≈ 0.019 (for outcome 4)
|0.098 - 1/6| = 0.098 - 0.167 ≈ 0.069 (for outcome 6)
|0.246 - 1/6| = 0.246 - 0.167 ≈ 0.079 (for outcome 8)
|0.213 - 1/6| = 0.213 - 0.167 ≈ 0.046 (for outcome 10)
|0.131 - 1/6| = 0.131 - 0.167 ≈ 0.036 (for outcome 12)
The largest discrepancy is 0.079, which represents the outcome 8.
Therefore, the largest discrepancy between the experimental and expected probability of this experiment is 0.079.
wrong, its actually 8
Apologies for the mistake. Let's recalculate the largest discrepancy:
The expected probability of each outcome is 1/6 since there are 6 possible outcomes on the cube.
Total number of trials = 10 + 9 + 6 + 15 + 13 + 8 = 61
For outcomes 2, 4, 6, 8, 10, 12:
Experimental probability of 2 = 10/61 ≈ 0.164
Experimental probability of 4 = 9/61 ≈ 0.148
Experimental probability of 6 = 6/61 ≈ 0.098
Experimental probability of 8 = 15/61 ≈ 0.246
Experimental probability of 10 = 13/61 ≈ 0.213
Experimental probability of 12 = 8/61 ≈ 0.131
Now, we find the largest discrepancy between the experimental and expected probability:
|Experimental probability - Expected probability|:
|0.164 - 1/6| = 0.164 - 0.167 ≈ 0.003 (for outcome 2)
|0.148 - 1/6| = 0.148 - 0.167 ≈ 0.019 (for outcome 4)
|0.098 - 1/6| = 0.098 - 0.167 ≈ 0.069 (for outcome 6)
|0.246 - 1/6| = 0.246 - 0.167 ≈ 0.079 (for outcome 8)
|0.213 - 1/6| = 0.213 - 0.167 ≈ 0.046 (for outcome 10)
|0.131 - 1/6| = 0.131 - 0.167 ≈ 0.036 (for outcome 12)
The largest discrepancy is 0.079, which corresponds to outcome 8.
Therefore, the largest discrepancy between the experimental and expected probability of this experiment is 0.079. Thank you for pointing out the error!