Question
) A board game uses a spinner with three equal sections labeled A, B, and C. A player spins the wheel 60 times and records the outcomes:
A: 28 times
B: 15 times
C: 17 times
How does the experimental probability compare to the theoretical probability?
(4 Points)
The experimental probability matches the theoretical probability exactly.
The experimental probability for A is greater than the theoretical probability.
The experimental probability for B is greater than expected.
The experimental probability for C is greater than expected.
A: 28 times
B: 15 times
C: 17 times
How does the experimental probability compare to the theoretical probability?
(4 Points)
The experimental probability matches the theoretical probability exactly.
The experimental probability for A is greater than the theoretical probability.
The experimental probability for B is greater than expected.
The experimental probability for C is greater than expected.
Answers
GPT-4o mini
To compare the experimental probabilities with the theoretical probabilities, we first need to determine the theoretical probabilities for sections A, B, and C.
Since the spinner has three equal sections, the theoretical probability for each section is:
- Probability of A (P(A)) = 1/3 ≈ 0.3333
- Probability of B (P(B)) = 1/3 ≈ 0.3333
- Probability of C (P(C)) = 1/3 ≈ 0.3333
Next, we calculate the experimental probabilities based on the recorded outcomes:
1. For A:
- Experimental probability of A (P(A) experimental) = Number of A outcomes / Total spins = 28 / 60 ≈ 0.4667
2. For B:
- Experimental probability of B (P(B) experimental) = Number of B outcomes / Total spins = 15 / 60 = 0.25
3. For C:
- Experimental probability of C (P(C) experimental) = Number of C outcomes / Total spins = 17 / 60 ≈ 0.2833
Now we compare the experimental probabilities to the theoretical probabilities:
- For A:
- Experimental probability (0.4667) is greater than theoretical probability (0.3333).
- For B:
- Experimental probability (0.25) is less than theoretical probability (0.3333).
- For C:
- Experimental probability (0.2833) is less than theoretical probability (0.3333).
Based on these comparisons, we can conclude the following statements:
- The experimental probability for A is greater than the theoretical probability.
- The experimental probability for B is less than expected.
- The experimental probability for C is less than expected.
The most accurate selection from the options provided is:
**The experimental probability for A is greater than the theoretical probability.**
Since the spinner has three equal sections, the theoretical probability for each section is:
- Probability of A (P(A)) = 1/3 ≈ 0.3333
- Probability of B (P(B)) = 1/3 ≈ 0.3333
- Probability of C (P(C)) = 1/3 ≈ 0.3333
Next, we calculate the experimental probabilities based on the recorded outcomes:
1. For A:
- Experimental probability of A (P(A) experimental) = Number of A outcomes / Total spins = 28 / 60 ≈ 0.4667
2. For B:
- Experimental probability of B (P(B) experimental) = Number of B outcomes / Total spins = 15 / 60 = 0.25
3. For C:
- Experimental probability of C (P(C) experimental) = Number of C outcomes / Total spins = 17 / 60 ≈ 0.2833
Now we compare the experimental probabilities to the theoretical probabilities:
- For A:
- Experimental probability (0.4667) is greater than theoretical probability (0.3333).
- For B:
- Experimental probability (0.25) is less than theoretical probability (0.3333).
- For C:
- Experimental probability (0.2833) is less than theoretical probability (0.3333).
Based on these comparisons, we can conclude the following statements:
- The experimental probability for A is greater than the theoretical probability.
- The experimental probability for B is less than expected.
- The experimental probability for C is less than expected.
The most accurate selection from the options provided is:
**The experimental probability for A is greater than the theoretical probability.**