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 the expected probability, we need to calculate the expected probability first.
The total number of outcomes on the cube is 6 (2, 4, 6, 8, 10, 12). Each outcome has an equal probability of 1/6.
Expected probability for each outcome: 1/6 = 16.67%
Expected probability for getting an even number (2, 4, 6, 8, 10, or 12): 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 6/6 = 100%
Now, we can compare the expected and experimental probabilities:
Experimental probability for each outcome:
- For 2: 10/61 ≈ 16.39%
- For 4: 9/61 ≈ 14.75%
- For 6: 6/61 ≈ 9.84%
- For 8: 15/61 ≈ 24.59%
- For 10: 13/61 ≈ 21.31%
- For 12: 8/61 ≈ 13.11%
The largest discrepancy between the experimental and expected probability is for getting the number 8.
The experimental probability is 24.59% and the expected probability is 16.67%.
The discrepancy is |24.59 - 16.67| ≈ 7.92%
Therefore, the largest discrepancy between the experimental and expected probability in percent form to the nearest whole number is 8%.
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 smallest discrepancy between the experimental and the expected probability of this experiment? Write your answer in 3 decimal places, rounded to the nearest thousandth.
(1 point)