Need tossed a cube with faces numbered with 2, 4, 6, 8, 10, and 12. The results are recorded in the table. Outcome 2, 4, 6, 8, 10, 12; Frequency 10, 9, 6, 15, 13, 8; 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 largest discrepancy between the experimental and the expected probability, we first need to calculate the expected probability for each outcome.
The total number of trials in this experiment is 10 + 9 + 6 + 15 + 13 + 8 = 61.
The expected probability for each outcome can be calculated by dividing the frequency of each outcome by the total number of trials:
Expected Probability of 2 = 10/61 ≈ 0.164
Expected Probability of 4 = 9/61 ≈ 0.148
Expected Probability of 6 = 6/61 ≈ 0.098
Expected Probability of 8 = 15/61 ≈ 0.246
Expected Probability of 10 = 13/61 ≈ 0.213
Expected Probability of 12 = 8/61 ≈ 0.131
Next, we can calculate the experimental probability by dividing the frequency of each outcome by the total number of trials:
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
The largest discrepancy between the experimental and the expected probability is for an outcome of 10, where the experimental probability is 0.213 and the expected probability is 0.164.
To find the largest discrepancy as a percentage, we can calculate the difference between the experimental and expected probabilities for the outcome of 10 and divide by the expected probability:
(0.213 - 0.164) / 0.164 ≈ 0.298
Therefore, the largest discrepancy between the experimental and expected probability in this experiment is approximately 30%.