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 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. (1 point)
To find the largest discrepancy between the experimental and expected probability, we first need to calculate the expected probability for each outcome. The total number of trials is 10 + 9 + 6 + 15 + 13 + 8 = 61.
The expected probabilities are:
- Probability of getting a 2: 1/6 = 0.167
- Probability of getting a 4: 1/6 = 0.167
- Probability of getting a 6: 1/6 = 0.167
- Probability of getting an 8: 1/6 = 0.167
- Probability of getting a 10: 1/6 = 0.167
- Probability of getting a 12: 1/6 = 0.167
Now, we calculate the experimental probabilities by dividing the frequency of each outcome by the total number of trials:
- 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
The largest discrepancy between the experimental and expected probability is for the outcome of 8, where the experimental probability is 0.246 and the expected probability is 0.167. To find the percentage discrepancy, we calculate:
(0.246 - 0.167) / 0.167 ≈ 0.479
Rounded to the nearest whole number, the largest discrepancy is 48%.