To find the experimental probability of each outcome, we divide the frequency by the total number of trials, which is:
10 + 9 + 6 + 15 + 13 + 8 = 61
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
To find the expected probability of each outcome, we divide 1 by the number of possible outcomes, which is:
1/6 ≈ 0.167
Expected Probability of 2 = 0.167
Expected Probability of 4 = 0.167
Expected Probability of 6 = 0.167
Expected Probability of 8 = 0.167
Expected Probability of 10 = 0.167
Expected Probability of 12 = 0.167
To find the discrepancy between the experimental and expected probabilities, we subtract the expected probability from the experimental probability for each outcome, and take the absolute value of the difference. Then we find the largest discrepancy:
|Experimental Probability of 2 - Expected Probability of 2| = |0.164 - 0.167| ≈ 0.003
|Experimental Probability of 4 - Expected Probability of 4| = |0.148 - 0.167| ≈ 0.019
|Experimental Probability of 6 - Expected Probability of 6| = |0.098 - 0.167| ≈ 0.069
|Experimental Probability of 8 - Expected Probability of 8| = |0.246 - 0.167| ≈ 0.079
|Experimental Probability of 10 - Expected Probability of 10| = |0.213 - 0.167| ≈ 0.046
|Experimental Probability of 12 - Expected Probability of 12| = |0.131 - 0.167| ≈ 0.036
The largest discrepancy is 0.079, which corresponds to the outcome of 8. To find the discrepancy as a percentage, we divide it by the expected probability and multiply by 100:
0.079/0.167 x 100 ≈ 47 (rounded to the nearest whole number)
Therefore, the largest discrepancy between the experimental and expected probability of this experiment is 47%.
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? The answer needs to be in percent form to the nearest whole number.
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