Answer :
To determine which scenario produces the given uniform probability model where there are five outcomes with each outcome having a probability of 20.0%, we'll analyze the given scenarios one by one.
### Scenario a: Rolling a six-sided number cube
- A six-sided number cube (traditional die) has six faces numbered from 1 to 6.
- The probability of landing on any one face is [tex]\( \frac{1}{6} \approx 16.67\% \)[/tex], since all outcomes are equally likely.
- We need five outcomes with each having a 20.0% probability.
- Since a six-sided die has six possible outcomes and none of them fit the required probability model, this scenario does not match our model.
### Scenario b: Randomly picking one of the numbers 1 through 10 from a hat
- When you randomly pick one number from ten possible numbers (1 through 10), each of the 10 numbers has an equal probability of being selected.
- The probability of selecting any one number from 10 numbers is [tex]\( \frac{1}{10} = 10.0\% \)[/tex].
- We need five outcomes with each having a 20.0% probability.
- Since there are ten possible outcomes and none of them fit the required probability model, this scenario does not match our model either.
### Conclusion
After analyzing both scenarios, neither the six-sided die nor randomly picking a number from 1 to 10 produces the uniform probability model with five outcomes, each having a 20.0% probability. Therefore, neither scenario a) nor scenario b) is correct.
### Scenario a: Rolling a six-sided number cube
- A six-sided number cube (traditional die) has six faces numbered from 1 to 6.
- The probability of landing on any one face is [tex]\( \frac{1}{6} \approx 16.67\% \)[/tex], since all outcomes are equally likely.
- We need five outcomes with each having a 20.0% probability.
- Since a six-sided die has six possible outcomes and none of them fit the required probability model, this scenario does not match our model.
### Scenario b: Randomly picking one of the numbers 1 through 10 from a hat
- When you randomly pick one number from ten possible numbers (1 through 10), each of the 10 numbers has an equal probability of being selected.
- The probability of selecting any one number from 10 numbers is [tex]\( \frac{1}{10} = 10.0\% \)[/tex].
- We need five outcomes with each having a 20.0% probability.
- Since there are ten possible outcomes and none of them fit the required probability model, this scenario does not match our model either.
### Conclusion
After analyzing both scenarios, neither the six-sided die nor randomly picking a number from 1 to 10 produces the uniform probability model with five outcomes, each having a 20.0% probability. Therefore, neither scenario a) nor scenario b) is correct.
