Joseph to a cube with faces numbered with 246 810 and 12 the results are recorded in the table. What is the largest discrepancy between the experimental and the expected probability a dis experiment the answer needs to be in form to the nearest home number in the table we have for the number two it would be 10 for the number four. It would be nine and the number six it would be six number eight is 15 number 10 is 13 and number 12 is eight.
To find the largest discrepancy between the experimental and expected probability, we first need to calculate the expected probability of each number based on a fair six-sided die. Since we have a cube numbered with 2, 4, 6, 8, 10, and 12, we need to figure out the probability of each number showing up.
The expected probabilities for each number are as follows:
- Number 2: 1/6
- Number 4: 1/6
- Number 6: 1/6
- Number 8: 1/6
- Number 10: 1/6
- Number 12: 1/6
Next, we need to calculate the experimental probabilities based on the results recorded in the table. From the table, we can calculate that the experimental probabilities are:
- Number 2: 10 times
- Number 4: 9 times
- Number 6: 6 times
- Number 8: 15 times
- Number 10: 13 times
- Number 12: 8 times
Now, we can calculate the discrepancies by finding the absolute difference between the experimental and expected probabilities for each number:
- For number 2: |1/6 - 10/54| = 0.0185
- For number 4: |1/6 - 9/54| = 0.0185
- For number 6: |1/6 - 6/54| = 0.0556
- For number 8: |1/6 - 15/54| = 0.0926
- For number 10: |1/6 - 13/54| = 0.0556
- For number 12: |1/6 - 8/54| = 0.0370
The largest discrepancy is for number 8, with a value of 0.0926, which corresponds to 9 as the nearest whole number. Therefore, the largest discrepancy between the experimental and expected probability is 9.