To find the expected probability for each outcome, we divide the total frequency (which is the sum of all frequencies) by 6 (since there are 6 possible outcomes):
Expected probability of getting 2: (10+9+6+15+13+8)/6 = 4.1666667
Expected probability of getting 4: (10+9+6+15+13+8)/6 = 4.1666667
Expected probability of getting 6: (10+9+6+15+13+8)/6 = 4.1666667
Expected probability of getting 8: (10+9+6+15+13+8)/6 = 4.1666667
Expected probability of getting 10: (10+9+6+15+13+8)/6 = 4.1666667
Expected probability of getting 12: (10+9+6+15+13+8)/6 = 4.1666667
To find the discrepancy, we subtract the expected probability from the actual frequency for each outcome, take the absolute value, and add them up:
Discrepancy for outcome 2: |10 - 4.1666667| = 5.8333333
Discrepancy for outcome 4: |9 - 4.1666667| = 4.8333333
Discrepancy for outcome 6: |6 - 4.1666667| = 1.8333333
Discrepancy for outcome 8: |15 - 4.1666667| = 10.8333333
Discrepancy for outcome 10: |13 - 4.1666667| = 8.8333333
Discrepancy for outcome 12: |8 - 4.1666667| = 3.8333333
The smallest discrepancy is 1.8333333, which corresponds to outcome 6. Rounding to the nearest thousandth gives us an answer of 1.833.
Outcomes. 2. 4. 6. 8. 10. 12
Frequency 10 9. 6. 15 13. 8
What is the smallest discrepancy between the experiment and the expected probability of this experiment? Write answer in a 3 decimal places, rounded to the nearest thousandth.
1 answer