Question
terrell argues that because the spinner shown is divided into equal areas, landing on a color can be represented by a uniform probability models. His math partners says that it is represented by a non-uniform models. who is correct? explain
Answers
GPT-4o mini
To determine whether Terrell or his math partner is correct regarding the probability model that represents landing on a color when spinning a spinner divided into equal areas, we need to consider how probabilities are assigned based on the layout of the spinner.
1. **Uniform Probability Model**: A uniform probability model applies when all outcomes are equally likely. If the spinner is divided into equal sections (for example, if a spinner has four equal sections colored red, blue, green, and yellow), each color has an equal chance of being landed on. In this case, the probability of landing on any specific color is the same:
- Probability of red = 1/4
- Probability of blue = 1/4
- Probability of green = 1/4
- Probability of yellow = 1/4
This situation is a perfect example of a uniform probability model because each outcome (color) occurs with the same likelihood.
2. **Non-Uniform Probability Model**: A non-uniform probability model would be appropriate if the spinner were divided into sections of unequal areas. For example, if one section was twice the size of another, the probability of landing on that larger area would be greater than the probability of landing on the smaller one.
In conclusion, if Terrell is describing a spinner that is indeed divided into equal areas, **he is correct** that it can be represented by a uniform probability model. If there were unequal areas, then his partner would be correct in referencing a non-uniform model. The key factor is whether the areas of the spinner are equal or not.
1. **Uniform Probability Model**: A uniform probability model applies when all outcomes are equally likely. If the spinner is divided into equal sections (for example, if a spinner has four equal sections colored red, blue, green, and yellow), each color has an equal chance of being landed on. In this case, the probability of landing on any specific color is the same:
- Probability of red = 1/4
- Probability of blue = 1/4
- Probability of green = 1/4
- Probability of yellow = 1/4
This situation is a perfect example of a uniform probability model because each outcome (color) occurs with the same likelihood.
2. **Non-Uniform Probability Model**: A non-uniform probability model would be appropriate if the spinner were divided into sections of unequal areas. For example, if one section was twice the size of another, the probability of landing on that larger area would be greater than the probability of landing on the smaller one.
In conclusion, if Terrell is describing a spinner that is indeed divided into equal areas, **he is correct** that it can be represented by a uniform probability model. If there were unequal areas, then his partner would be correct in referencing a non-uniform model. The key factor is whether the areas of the spinner are equal or not.