Question
A spinner containing four equal sections labels with Blue 1, Purple 2, Green 3, and Red 4 was spun 200 times. Select all of the following that are true statements. Responses The theoretical probability of landing on Red 4, is more than the experimental probability of landing on Green 3. The theoretical probability of landing on Red 4, is more than the experimental probability of landing on Green 3. The experimental probability of landing on Red 4 is more than the theoretical probability of landing on Blue 1. The experimental probability of landing on Red 4 is more than the theoretical probability of landing on Blue 1. The experimental probability of landing on Purple 2 is more than the theoretical probability of landing on Blue 1. The experimental probability of landing on Purple 2 is more than the theoretical probability of landing on Blue 1. The theoretical probability of landing on Blue 1 is more than the experimental probability of landing on Red 4. The theoretical probability of landing on Blue 1 is more than the experimental probability of landing on Red 4. Skip to navigation
Answers
GPT-4o mini
To assess the truth of the statements regarding the probabilities of the spinner outcomes, let's first determine the theoretical probabilities for each section of the spinner.
The spinner has four equal sections:
- Blue 1
- Purple 2
- Green 3
- Red 4
Since there are four sections, the theoretical probability of landing on each section is:
- P(Blue 1) = 1/4 = 0.25
- P(Purple 2) = 1/4 = 0.25
- P(Green 3) = 1/4 = 0.25
- P(Red 4) = 1/4 = 0.25
Now, let's analyze each of the statements. We don't have the specific experimental outcomes, but we can make logical comparisons based on the theoretical probabilities.
1. **The theoretical probability of landing on Red 4 is more than the experimental probability of landing on Green 3.**
- This can be true or false; we need the experimental outcome of Green 3 to determine this.
2. **The theoretical probability of landing on Red 4 is more than the experimental probability of landing on Green 3.**
- This is identical to the first statement in wording and interpretation, hence it is subject to the same uncertainty.
3. **The experimental probability of landing on Red 4 is more than the theoretical probability of landing on Blue 1.**
- If the experimental probability of Red 4 is over 0.25, this statement can be true; otherwise, it can be false.
4. **The experimental probability of landing on Red 4 is more than the theoretical probability of landing on Blue 1.**
- This statement repeats the previous one, hence subject to the same uncertainty.
5. **The experimental probability of landing on Purple 2 is more than the theoretical probability of landing on Blue 1.**
- If Purple 2's experimental probability exceeds 0.25, then this can be true; otherwise, it can be false.
6. **The experimental probability of landing on Purple 2 is more than the theoretical probability of landing on Blue 1.**
- This is a repeat with similar uncertainty.
7. **The theoretical probability of landing on Blue 1 is more than the experimental probability of landing on Red 4.**
- Unless the experimental outcome for Red 4 is unusually high, this is likely false as both have a theoretical probability of 0.25.
8. **The theoretical probability of landing on Blue 1 is more than the experimental probability of landing on Red 4.**
- Similar to the previous statement, it largely holds under the same logic.
Since we lack specific experimental probabilities, we can only conclude that many of these statements are undetermined without the data.
However, we do know the theoretical probabilities:
- Theoretical probability for all outcomes (Blue 1, Purple 2, Green 3, Red 4) is 0.25.
Therefore, we can't definitively say which of the statements are true or false concerning the experimental probabilities, as they depend on specific results from the 200 spins. If the experimental counts are available, we would be able to refute or confirm each statement accordingly.
The spinner has four equal sections:
- Blue 1
- Purple 2
- Green 3
- Red 4
Since there are four sections, the theoretical probability of landing on each section is:
- P(Blue 1) = 1/4 = 0.25
- P(Purple 2) = 1/4 = 0.25
- P(Green 3) = 1/4 = 0.25
- P(Red 4) = 1/4 = 0.25
Now, let's analyze each of the statements. We don't have the specific experimental outcomes, but we can make logical comparisons based on the theoretical probabilities.
1. **The theoretical probability of landing on Red 4 is more than the experimental probability of landing on Green 3.**
- This can be true or false; we need the experimental outcome of Green 3 to determine this.
2. **The theoretical probability of landing on Red 4 is more than the experimental probability of landing on Green 3.**
- This is identical to the first statement in wording and interpretation, hence it is subject to the same uncertainty.
3. **The experimental probability of landing on Red 4 is more than the theoretical probability of landing on Blue 1.**
- If the experimental probability of Red 4 is over 0.25, this statement can be true; otherwise, it can be false.
4. **The experimental probability of landing on Red 4 is more than the theoretical probability of landing on Blue 1.**
- This statement repeats the previous one, hence subject to the same uncertainty.
5. **The experimental probability of landing on Purple 2 is more than the theoretical probability of landing on Blue 1.**
- If Purple 2's experimental probability exceeds 0.25, then this can be true; otherwise, it can be false.
6. **The experimental probability of landing on Purple 2 is more than the theoretical probability of landing on Blue 1.**
- This is a repeat with similar uncertainty.
7. **The theoretical probability of landing on Blue 1 is more than the experimental probability of landing on Red 4.**
- Unless the experimental outcome for Red 4 is unusually high, this is likely false as both have a theoretical probability of 0.25.
8. **The theoretical probability of landing on Blue 1 is more than the experimental probability of landing on Red 4.**
- Similar to the previous statement, it largely holds under the same logic.
Since we lack specific experimental probabilities, we can only conclude that many of these statements are undetermined without the data.
However, we do know the theoretical probabilities:
- Theoretical probability for all outcomes (Blue 1, Purple 2, Green 3, Red 4) is 0.25.
Therefore, we can't definitively say which of the statements are true or false concerning the experimental probabilities, as they depend on specific results from the 200 spins. If the experimental counts are available, we would be able to refute or confirm each statement accordingly.