Jude 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? The answer needs to be in percent form to the nearest whole number

Answer 1

To find the expected probability of each number appearing, we divide the number of occurrences of each face by the total number of throws. The expected probabilities are as follows:

- Expected probability of rolling a 2: 1/6
- Expected probability of rolling a 4: 1/6
- Expected probability of rolling a 6: 1/6
- Expected probability of rolling an 8: 1/6
- Expected probability of rolling a 10: 1/6
- Expected probability of rolling a 12: 1/6

Now let's calculate the experimental probabilities based on the results recorded in the table:

- Experimental probability of rolling a 2: 30/100 = 0.3
- Experimental probability of rolling a 4: 10/100 = 0.1
- Experimental probability of rolling a 6: 20/100 = 0.2
- Experimental probability of rolling an 8: 15/100 = 0.15
- Experimental probability of rolling a 10: 15/100 = 0.15
- Experimental probability of rolling a 12: 10/100 = 0.1

Now we calculate the discrepancies for each number by taking the absolute difference between the expected and experimental probabilities:

- Discrepancy for 2: |1/6 - 0.3| = 0.1333
- Discrepancy for 4: |1/6 - 0.1| = 0.0667
- Discrepancy for 6: |1/6 - 0.2| = 0.0667
- Discrepancy for 8: |1/6 - 0.15| = 0.0167
- Discrepancy for 10: |1/6 - 0.15| = 0.0167
- Discrepancy for 12: |1/6 - 0.1| = 0.0667

The smallest discrepancy is 0.0167, which corresponds to rolling an 8 or 10. Converting this into percent form to the nearest whole number gives us 2%. So, the smallest discrepancy between the experimental and expected probability of this experiment is 2%.