Someone tossed a cube with faces numbered with two, four, six, eight, 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. The frequency of two is 10, the frequency of 4 is 9, the frequency of 6 is 6, frequency of 8 is 15, the frequency of 10 is 13, and the frequency of 12 is 8
To find the expected probability for each number, we first need to determine the total number of throws in the experiment.
Total number of throws = 10 + 9 + 6 + 15 + 13 + 8 = 61
Expected probability of getting a 2: (1/6) = 1/6 = 0.167
Expected probability of getting a 4: (1/6) = 1/6 = 0.167
Expected probability of getting a 6: (1/6) = 1/6 = 0.167
Expected probability of getting an 8: (1/6) = 1/6 = 0.167
Expected probability of getting a 10: (1/6) = 1/6 = 0.167
Expected probability of getting a 12: (1/6) = 1/6 = 0.167
Now we can calculate the experimental and expected probabilities for each number:
Experimental probability of getting a 2: 10/61 ≈ 0.164
Experimental probability of getting a 4: 9/61 ≈ 0.148
Experimental probability of getting a 6: 6/61 ≈ 0.098
Experimental probability of getting an 8: 15/61 ≈ 0.246
Experimental probability of getting a 10: 13/61 ≈ 0.213
Experimental probability of getting a 12: 8/61 ≈ 0.131
Now we can calculate the discrepancies between the experimental and expected probabilities for each number:
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 largest discrepancy is 0.079, which corresponds to getting an 8. To convert to a percentage and round to the nearest whole number, the largest discrepancy is 8%.