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.
To find the expected probability of each number appearing on the cube, we first calculate the total number of possible outcomes. Since there are 6 numbers on the cube, the total number of outcomes is 6.
The expected probability of each number is 1/6, as there is an equal chance of each number appearing.
Now, we calculate the experimental probability based on the results recorded:
Number 2 appeared 3 times
Number 4 appeared 2 times
Number 6 appeared 4 times
Number 8 appeared 5 times
Number 10 appeared 2 times
Number 12 appeared 4 times
The total number of outcomes recorded is 20.
Now we calculate the experimental probability of each number:
- Number 2: 3/20
- Number 4: 2/20
- Number 6: 4/20
- Number 8: 5/20
- Number 10: 2/20
- Number 12: 4/20
Now we find the discrepancy between the experimental and expected probability for each number:
- Number 2: |1/6 - 3/20| = |0.167 - 0.150| = 0.017
- Number 4: |1/6 - 2/20| = |0.167 - 0.100| = 0.067
- Number 6: |1/6 - 4/20| = |0.167 - 0.200| = 0.033
- Number 8: |1/6 - 5/20| = |0.167 - 0.250| = 0.083
- Number 10: |1/6 - 2/20| = |0.167 - 0.100| = 0.067
- Number 12: |1/6 - 4/20| = |0.167 - 0.200| = 0.033
The smallest discrepancy is 0.017, which occurs for the number 2.
Therefore, the smallest discrepancy between the experimental and expected probability is 0.017.