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.
To find the expected probability, we need to add up the frequencies and divide each frequency by the total:
Total frequency = 10 + 9 + 6 + 15 + 13 + 8 = 61
Expected probability of rolling a 2: 10/61 = 0.1639 or 16%
Expected probability of rolling a 4: 9/61 = 0.1475 or 15%
Expected probability of rolling a 6: 6/61 = 0.0984 or 10%
Expected probability of rolling an 8: 15/61 = 0.2459 or 25%
Expected probability of rolling a 10: 13/61 = 0.2131 or 21%
Expected probability of rolling a 12: 8/61 = 0.1311 or 13%
To find the largest discrepancy between the experimental and expected probability, we need to compare each probability and find the largest absolute difference. For example, the experimental probability of rolling a 2 is 10/61 = 0.1639, which is 16% in percent form. The absolute difference between the experimental and expected probability of rolling a 2 is:
|0.1639 - 0.16| = 0.0039 or 0.39%
We can do the same calculation for each outcome and find the largest absolute difference. The largest absolute difference is between the experimental and expected probability of rolling an 8:
|0.2459 - 0.2459| = 0 or 0%
Therefore, the largest discrepancy between the experimental and expected probability of rolling the cube is 0%, which means the experimental and expected probabilities are the same for rolling an 8.