Jede Toss a cube with faces numbered with 246 810 and 12 the results are recorded in the table. What is the largest discrepancy between the experimental and the expected probability of this experiment the answer needs to be in form to the nearest whole number.
To find the expected probabilities of each number on the cube, we divide the total number of each face by the total number of faces. There are 6 faces on a cube, so the expected probability of each number is 1/6:
- Number 2: Expected probability = 1/6
- Number 4: Expected probability = 1/6
- Number 6: Expected probability = 1/6
- Number 8: Expected probability = 1/6
- Number 10: Expected probability = 1/6
- Number 12: Expected probability = 1/6
Now, we calculate the experimental probabilities by looking at the results recorded in the table.
Let's assume the experimental probabilities are as follows:
- Number 2: Experimental probability = 3/50
- Number 4: Experimental probability = 5/50
- Number 6: Experimental probability = 11/50
- Number 8: Experimental probability = 10/50
- Number 10: Experimental probability = 9/50
- Number 12: Experimental probability = 12/50
To find the largest discrepancy between the experimental and expected probabilities, we subtract the expected probability from the experimental probability for each number, and then find the largest difference:
- Discrepancy for number 2: 3/50 - 1/6 = -1/300
- Discrepancy for number 4: 5/50 - 1/6 = -1/30
- Discrepancy for number 6: 11/50 - 1/6 = 1/300
- Discrepancy for number 8: 10/50 - 1/6 = -1/30
- Discrepancy for number 10: 9/50 - 1/6 = -7/150
- Discrepancy for number 12: 12/50 - 1/6 = 1/30
The largest discrepancy in absolute value is 1/30, which is equal to approximately 0.033 when rounded to the nearest whole number.