To compare the experimental probability with the theoretical probability for the spinner, we need to calculate both.
Theoretical Probability: Since the spinner has three equal sections labeled A, B, and C, the theoretical probability of landing on each section is:
- \( P(A) = \frac{1}{3} \)
- \( P(B) = \frac{1}{3} \)
- \( P(C) = \frac{1}{3} \)
Experimental Probability: Experimental probability is calculated based on the outcomes from the spins. The total number of spins is 60, and the outcomes are recorded as follows:
- A occurred 28 times
- B occurred 15 times
- C occurred 17 times
The experimental probabilities can be calculated as follows:
- \( P(A)_{experimental} = \frac{28}{60} = \frac{14}{30} \approx 0.4667 \)
- \( P(B)_{experimental} = \frac{15}{60} = \frac{1}{4} = 0.25 \)
- \( P(C)_{experimental} = \frac{17}{60} \approx 0.2833 \)
Comparison:
-
Theoretical Probability of A: \( \frac{1}{3} \approx 0.3333 \)
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Experimental Probability of A: \( \approx 0.4667 \)
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Theoretical Probability of B: \( \frac{1}{3} \approx 0.3333 \)
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Experimental Probability of B: \( 0.25 \)
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Theoretical Probability of C: \( \frac{1}{3} \approx 0.3333 \)
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Experimental Probability of C: \( \approx 0.2833 \)
Conclusion:
- For section A, the experimental probability (approximately 0.4667) is higher than the theoretical probability (approximately 0.3333).
- For section B, the experimental probability (0.25) is lower than the theoretical probability (approximately 0.3333).
- For section C, the experimental probability (approximately 0.2833) is lower than the theoretical probability (approximately 0.3333).
Overall, the experimental probabilities show some deviation from the theoretical probabilities, which can occur due to the randomness of the spins.