Answer:
The experimental probability of rolling an odd number is 60%, which is 10% more than the theoretical probability.
Step-by-step explanation:
The complete question is:
Type the correct answer in each box. Use numerals instead of words. If necessary, use/ for the fraction bar(s).
A special 8-sided die is marked with the numbers 1 to 8. It is rolled 20 times with these outcomes.
3, 4, 5, 2, 7, 1, 3, 7, 2, 6, 2, 1, 7, 3, 6, 1, 8, 3, 5, 6
The experimental probability of rolling an odd number is _%, which is _% more than the theoretical probability.
Solution:
The possible outcomes of rolling an 8-sided die are:
S = {1, 2, 3, 4, 5, 6, 7, 8}
The odd numbers are:
Odd = {1, 3, 5, 7} = 4 outcomes
The theoretical probability of rolling an odd number is:
![P_{T}(\text{Odd})=\farc{4}{8}=\frac{1}{2}=50\%](https://tex.z-dn.net/?f=P_%7BT%7D%28%5Ctext%7BOdd%7D%29%3D%5Cfarc%7B4%7D%7B8%7D%3D%5Cfrac%7B1%7D%7B2%7D%3D50%5C%25)
Now from the given 20 outcomes the odd values are:
Odd = {3, 5, 7, 1, 3, 7, 1, 7, 3, 1, 3, 5} = 12 outcomes
Compute the experimental probability of rolling an odd number as follows:
![P_{E}(\text{Odd})=\frac{12}{20}=\frac{3}{5}=60\%](https://tex.z-dn.net/?f=P_%7BE%7D%28%5Ctext%7BOdd%7D%29%3D%5Cfrac%7B12%7D%7B20%7D%3D%5Cfrac%7B3%7D%7B5%7D%3D60%5C%25)
Thus, the experimental probability of rolling an odd number is 60%, which is 10% more than the theoretical probability.