Jede tossed a cube with faces numbered with 2, 4, 6, 8, 10, and 12. The results are 10, 9, 6, 15, 13, 8. 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 smallest discrepancy between the experimental and the expected probability, we need to calculate the probability of each outcome based on the total possible outcomes of 6.
Expected probabilities:
- P(2) = 1/6
- P(4) = 1/6
- P(6) = 1/6
- P(8) = 1/6
- P(10) = 1/6
- P(12) = 1/6
Experimental probabilities:
- P(10) = 1/6
- P(9) = 0/6
- P(6) = 1/6
- P(15) = 0/6
- P(13) = 0/6
- P(8) = 1/6
Now, we calculate the absolute difference between the experimental and expected probabilities for each outcome:
|P(10) - P(10)| = |1/6 - 1/6| = 0
|P(9) - P(0)| = |0 - 1/6| = 1/6
|P(6) - P(6)| = |1/6 - 1/6| = 0
|P(15) - P(0)| = |0 - 1/6| = 1/6
|P(13) - P(0)| = |0 - 1/6| = 1/6
|P(8) - P(8)| = |1/6 - 1/6| = 0
The smallest discrepancy is 1/6.
Therefore, the smallest discrepancy between the experimental and expected probability of this experiment is 0.167 (rounded to 3 decimal places).