To compare the theoretical and experimental probabilities for the letters on the spinner, we first need the theoretical probabilities of landing on each letter. We will assume that the spinner is divided evenly between the letters A, B, C, and D, with each letter having an equal chance of being selected.
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Theoretical Probability: Since there are 4 letters, the theoretical probability for each letter (A, B, C, and D) is: \[ P(A) = P(B) = P(C) = P(D) = \frac{1}{4} = 0.25 \]
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Experimental Probability: We can calculate the experimental probability for each letter based on the frequency of spins:
- For A: \[ \text{Experimental Probability of A} = \frac{36}{180} = 0.20 \]
- For B: \[ \text{Experimental Probability of B} = \frac{48}{180} = 0.2667 \approx 0.27 \]
- For C: \[ \text{Experimental Probability of C} = \frac{51}{180} = 0.2833 \approx 0.28 \]
- For D: \[ \text{Experimental Probability of D} = \frac{45}{180} = 0.25 \]
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Comparison: Now we can summarize and compare the theoretical and experimental probabilities for each letter:
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Letter A:
- Theoretical Probability: 0.25
- Experimental Probability: 0.20
- Conclusion: The experimental probability of A is lower than the theoretical probability.
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Letter B:
- Theoretical Probability: 0.25
- Experimental Probability: 0.27
- Conclusion: The experimental probability of B is higher than the theoretical probability.
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Letter C:
- Theoretical Probability: 0.25
- Experimental Probability: 0.28
- Conclusion: The experimental probability of C is higher than the theoretical probability.
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Letter D:
- Theoretical Probability: 0.25
- Experimental Probability: 0.25
- Conclusion: The experimental probability of D equals the theoretical probability.
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In summary, we can say:
- The experimental probability of A is less than its theoretical probability.
- The experimental probabilities of B and C are greater than their theoretical probabilities.
- The experimental probability of D matches its theoretical probability.
Therefore, if you choose one of the letters, you can make statements like:
- "The experimental probability of A (0.20) is less than the theoretical probability (0.25)."
- "The experimental probability of B (0.27) is greater than the theoretical probability (0.25)."
- "The experimental probability of C (0.28) is greater than the theoretical probability (0.25)."
- "The experimental probability of D (0.25) is equal to its theoretical probability (0.25)."