Jede tossed a cube with faces numbered with 2, 4, 6, 8, 10, and 12. The results are recorded
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.
Outcomes. 2 4 6 8 10 12
Frequency 10 9 6 15 13 8
To find the expected probability, we need to divide the total number of trials by 6 (since there are 6 possible outcomes).
Total number of trials = 10 + 9 + 6 + 15 + 13 + 8 = 61
Expected probability = 1/6 ≈ 0.167
Now, we can calculate the experimental probability for each outcome by dividing the frequency of that outcome by the total number of trials.
Experimental probability for 2: 10/61 ≈ 0.164
Experimental probability for 4: 9/61 ≈ 0.148
Experimental probability for 6: 6/61 ≈ 0.098
Experimental probability for 8: 15/61 ≈ 0.246
Experimental probability for 10: 13/61 ≈ 0.213
Experimental probability for 12: 8/61 ≈ 0.131
The discrepancies between the experimental and expected probabilities are as follows:
For 2: |0.164 - 0.167| = 0.003
For 4: |0.148 - 0.167| = 0.019
For 6: |0.098 - 0.167| = 0.069
For 8: |0.246 - 0.167| = 0.079
For 10: |0.213 - 0.167| = 0.046
For 12: |0.131 - 0.167| = 0.036
The smallest discrepancy is 0.003.