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.
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I apologize for the mistake in the previous calculation. Let's correct that:
The expected probability for each number is 1/6 ≈ 16.67%.
From the experimental results:
- Number 2 appeared 3 times out of 30 trials, which is 3/30 = 0.1 = 10%
- Number 4 appeared 4 times out of 30 trials, which is 4/30 = 0.1333 ≈ 13.33%
- Number 6 appeared 5 times out of 30 trials, which is 5/30 = 0.1666 ≈ 16.67%
- Number 8 appeared 6 times out of 30 trials, which is 6/30 = 0.2 = 20%
- Number 10 appeared 8 times out of 30 trials, which is 8/30 = 0.2666 ≈ 26.67%
- Number 12 appeared 4 times out of 30 trials, which is 4/30 = 0.1333 ≈ 13.33%
Now, let's find the discrepancies:
- For number 10: |26.67% - 16.67%| = 10%
- For number 8: |20% - 16.67%| = 3.33%
- For number 6: |16.67% - 16.67%| = 0%
- For number 4: |13.33% - 16.67%| = 3.33%
- For number 2: |10% - 16.67%| = 6.67%
- For number 12: |13.33% - 16.67%| = 3.33%
The largest discrepancy between the experimental and expected probability is 10%. Thank you for your patience, and I appreciate your understanding.
To find the expected probability of each number appearing on the cube, we note that there are 6 sides and each number appears once. Therefore, the expected probability of each number is 1/6 or approximately 16.67%.
Next, let's calculate the experimental probabilities based on the results in the table:
- Number 2: 3/30 = 0.1 = 10%
- Number 4: 4/30 ≈ 0.1333 = 13.33%
- Number 6: 5/30 = 0.1666 ≈ 16.67%
- Number 8: 6/30 = 0.2 = 20%
- Number 10: 8/30 = 0.2666 ≈ 26.67%
- Number 12: 4/30 ≈ 0.1333 = 13.33%
Now, we can find the largest discrepancy between the experimental and expected probabilities:
- For number 10: |26.67% - 16.67%| = 10%
- For number 8: |20% - 16.67%| ≈ 3.33%
- For number 6: |16.67% - 16.67%| = 0%
- For number 4: |13.33% - 16.67%| ≈ 3.33%
- For number 2: |10% - 16.67%| = 6.67%
- For number 12: |13.33% - 16.67%| ≈ 3.33%
The largest discrepancy between the experimental and expected probability is 10%.