Jefe tossed a cube with faces numbered with 2,4,8,10, and 12. The results are recorded in the table. What is the smallest discrepancy between the experimental and expected probability of this experiment? Write your answer in 3 decimal places, rounded to the nearest thousandths. Outcomes:2, 4, 6, 19, 12; Frequency: 10, 9, 6, 15, 13, 8
To find the experimental probability for each outcome, we divide the frequency of each outcome by the total number of trials:
Total number of trials = 10 + 9 + 6 + 15 + 13 + 8 = 61
Experimental probability of getting 2: 10/61 ≈ 0.164
Experimental probability of getting 4: 9/61 ≈ 0.148
Experimental probability of getting 6: 6/61 ≈ 0.098
Experimental probability of getting 10: 15/61 ≈ 0.246
Experimental probability of getting 12: 13/61 ≈ 0.213
Now, let's calculate the expected probability of each outcome:
Expected probability of getting 2: 1/5 = 0.2
Expected probability of getting 4: 1/5 = 0.2
Expected probability of getting 6: 1/5 = 0.2
Expected probability of getting 19: 1/5 = 0.2
Expected probability of getting 12: 1/5 = 0.2
The discrepancy between the experimental and expected probability for each outcome is:
|0.164 - 0.2| = 0.036
|0.148 - 0.2| = 0.052
|0.098 - 0.2| = 0.102
|0.246 - 0.2| = 0.046
|0.213 - 0.2| = 0.013
The smallest discrepancy is 0.013.