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.
10
9
6
15
13
8
The expected probability of each number coming up when tossing a fair six-sided die is 1/6 or approximately 0.167.
Now we can calculate the experimental probability of each number coming up:
- Number 2 came up 0 times out of 6, so experimental probability is 0/6 = 0.
- Number 4 came up 1 time out of 6, so experimental probability is 1/6 = 0.167.
- Number 6 came up 2 times out of 6, so experimental probability is 2/6 = 0.333.
- Number 8 came up 0 times out of 6, so experimental probability is 0/6 = 0.
- Number 10 came up 2 times out of 6, so experimental probability is 2/6 = 0.333.
- Number 12 came up 1 time out of 6, so experimental probability is 1/6 = 0.167.
The discrepancy between the experimental and expected probabilities for each number is:
- For number 2: |0 - 0.167| = 0.167
- For number 4: |0.167 - 0.167| = 0
- For number 6: |0.333 - 0.167| = 0.167
- For number 8: |0 - 0.167| = 0.167
- For number 10: |0.333 - 0.167| = 0.167
- For number 12: |0.167 - 0.167| = 0
The smallest discrepancy is 0.167, rounded to three decimal places, this is equal to 0.167.