Use the table to answer the question. 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. (1 point).
To find the expected probability, we first find the total number of outcomes, which is the sum of all frequencies:
Total number of outcomes = 10 + 9 + 6 + 15 + 13 + 8 = 61
Next, we find the probability of each outcome by dividing the frequency of each outcome by the total number of outcomes:
Probability of 2 = 10/61 ≈ 0.164
Probability of 4 = 9/61 ≈ 0.148
Probability of 6 = 6/61 ≈ 0.098
Probability of 8 = 15/61 ≈ 0.246
Probability of 10 = 13/61 ≈ 0.213
Probability of 12 = 8/61 ≈ 0.131
The experimental probability is the actual frequency divided by the total number of outcomes.
Next, we find the discrepancy for each outcome by taking the absolute difference between the experimental probability and the expected probability:
|0.164 - 0.167| = 0.003
|0.148 - 0.148| = 0
|0.098 - 0.098| = 0
|0.246 - 0.246| = 0
|0.213 - 0.213| = 0
|0.131 - 0.131| = 0
The smallest discrepancy is 0.003. Therefore, the smallest discrepancy between the experimental and the expected probability of this experiment is 0.003 (rounded to the nearest thousandth).
you think thats a percentage
Apologies for the oversight. Let's convert the discrepancy into a percentage.
The discrepancy we found in the previous calculation was 0.003.
To convert this into a percentage, we multiply by 100:
0.003 * 100 = 0.3%
Therefore, the smallest discrepancy between the experimental and the expected probability of this experiment is 0.3% (rounded to the nearest thousandth).
its a whole number
I apologize for the error in my previous responses.
The smallest discrepancy between the experimental and the expected probability is when the outcome is 2.
The expected probability for the outcome 2 is 1 out of 6 or approximately 0.167 (16.7%).
The experimental probability for the outcome 2 is 10 out of 61 or approximately 0.164 (16.4%).
To find the discrepancy, we calculate the absolute difference between the experimental and expected probabilities for outcome 2:
|0.164 - 0.167| = 0.003
Therefore, the smallest discrepancy between the experimental and the expected probability of this experiment is 0.003.