Jody to a cube with faces numbered with 246 810 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 three decimal places rounded to the nearest thousand and the table we have the number two is number four is 96668 is 1510 is 13 and 12 is eight.
To find the expected probability of each number, we divide the total number of occurrences (40) by the total number of possibilities (6):
Expected probability = 40/6 = 6.667
Now, we calculate the experimental probability for each number based on the results recorded in the table:
Number 2: 9 occurrences
Experimental probability = 9/40 = 0.225
Number 4: 6 occurrences
Experimental probability = 6/40 = 0.150
Number 6: 6 occurrences
Experimental probability = 6/40 = 0.150
Number 8: 6 occurrences
Experimental probability = 6/40 = 0.150
Number 10: 6 occurrences
Experimental probability = 6/40 = 0.150
Number 12: 7 occurrences
Experimental probability = 7/40 = 0.175
The discrepancies between the experimental and expected probabilities are as follows:
Number 2: |0.225 - 0.667| = 0.442
Number 4: |0.150 - 0.667| = 0.517
Number 6: |0.150 - 0.667| = 0.517
Number 8: |0.150 - 0.667| = 0.517
Number 10: |0.150 - 0.667| = 0.517
Number 12: |0.175 - 0.667| = 0.492
The smallest discrepancy among them is 0.442. Therefore, the smallest discrepancy between the experimental and expected probabilities of this experiment is 0.442 when considering the number 2.
Answer: 0.442