To find the largest discrepancy between the experimental and expected probability, we first need to calculate the expected probability for each outcome. Since there are 6 possible outcomes on the cube, each outcome has a 1/6 probability.
Expected Probability for each outcome:
2: 1/6
4: 1/6
6: 1/6
8: 1/6
10: 1/6
12: 1/6
Next, we calculate the experimental probability using the frequency data provided in the table:
Experimental Probability for each outcome:
2: 10/61
4: 9/61
6: 6/61
8: 15/61
10: 13/61
12: 8/61
Now, we find the largest discrepancy by finding the difference between the experimental and expected probabilities for each outcome:
2: |(10/61) - (1/6)| = 17/183
4: |(9/61) - (1/6)| = 7/183
6: |(6/61) - (1/6)| = 5/61
8: |(15/61) - (1/6)| = 19/183
10: |(13/61) - (1/6)| = 29/183
12: |(8/61) - (1/6)| = 1/183
The largest discrepancy is 29/183. To find this in percent form, we convert it to a percentage:
(29/183) * 100 ≈ 15.8%
So, the largest discrepancy between the experimental and the expected probability is approximately 16%.
Question
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)
%
1 answer