Outcomes 2 4 6 8 10 12
Frequency 10 9 6 15 13 8
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.
no, 0.003
To find the expected probability for each outcome, we need to calculate the total number of possible outcomes and the probability of each outcome.
Total number of possible outcomes = 6 (since there are 6 faces on the cube)
Probability of each outcome = 1/6 (since each face is equally likely)
Expected frequency for each outcome = Probability of outcome * Total number of trials
Expected frequency for outcomes 2, 4, 6, 8, 10, 12:
2: (1/6) * 61 = 10.167
4: (1/6) * 61 = 10.167
6: (1/6) * 61 = 10.167
8: (1/6) * 61 = 10.167
10: (1/6) * 61 = 10.167
12: (1/6) * 61 = 10.167
Now, we can calculate the discrepancy for each outcome by taking the absolute difference between the experimental and expected frequency and then find the smallest discrepancy:
Discrepancy for outcomes 2, 4, 6, 8, 10, 12:
2: |10 - 10.167| = 0.167
4: |9 - 10.167| = 1.167
6: |6 - 10.167| = 4.167
8: |15 - 10.167| = 4.833
10: |13 - 10.167| = 2.833
12: |8 - 10.167| = 2.167
The smallest discrepancy between the experimental and expected probability is 0.167, which corresponds to the outcome 2. So, the answer is 0.167 (rounded to 3 decimal places).
I apologize for the oversight. Let's correct the calculations using the correct expected frequencies for each outcome:
Expected frequency for each outcome based on the probability (1/6) and total number of trials (61):
2: (1/6) * 61 = 10.167
4: (1/6) * 61 = 10.167
6: (1/6) * 61 = 10.167
8: (1/6) * 61 = 10.167
10: (1/6) * 61 = 10.167
12: (1/6) * 61 = 10.167
Now, we calculate the discrepancy for each outcome by taking the absolute difference between the experimental and expected frequency:
Discrepancy for outcomes 2, 4, 6, 8, 10, 12:
2: |10 - 10.167| = 0.167
4: |9 - 10.167| = 1.167
6: |6 - 10.167| = 4.167
8: |15 - 10.167| = 4.833
10: |13 - 10.167| = 2.833
12: |8 - 10.167| = 2.167
The smallest discrepancy between the experimental and expected probability is 0.167, which corresponds to the outcome 2. Therefore, the correct answer is 0.167 (rounded to 3 decimal places). Thank you for pointing out the error.