Need tossed a cube with faces numbered with 2.4.6.8.and 12 the results are recorded in the table. What is the largest and smallest discrepancy between the experimental and expected probability? Round to the nearest whole number.
outcomes: 2,4,6,8,10,12
frequency: 10,9,6,15,13,8
To calculate the expected probability, we first need to find the total number of throws:
10 + 9 + 6 + 15 + 13 + 8 = 61
Then we calculate the expected probability for each outcome:
- 2 and 12 have a probability of 1/6
- 4 and 10 have a probability of 1/3
- 6 and 8 have a probability of 1/4
Expected probabilities:
- 2 and 12: 61/6 = 10.167
- 4 and 10: 61/3 = 20.33
- 6 and 8: 61/4 = 15.25
Now we calculate the discrepancies:
- For 2: |10 - 10.167| = 0.167, rounded to 0
- For 4: |9 - 20.33| = 11.33, rounded to 11
- For 6: |6 - 15.25| = 9.25, rounded to 9
- For 8: |15 - 15.25| = 0.25, rounded to 0
- For 10: |13 - 20.33| = 7.33, rounded to 7
- For 12: |8 - 10.167| = 2.17, rounded to 2
The largest discrepancy is 11 and the smallest discrepancy is 0.