Subjects probability

Spinner Probability 4Ee6Ea

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1. **State the problem:** We have a spinner divided into 8 equal sectors, with 5 sectors shaded. It is spun 300 times, landing on a shaded region 168 times. We need to compare the theoretical probability of landing on a shaded region with the experimental probability and determine which is higher. 2. **Theoretical probability:** The theoretical probability is the chance of landing on a shaded sector based on the spinner's design. Since there are 5 shaded sectors out of 8 total sectors, the theoretical probability $P_{theoretical}$ is: $$P_{theoretical} = \frac{5}{8} = 0.625$$ 3. **Experimental probability:** The experimental probability is based on actual results from spinning the spinner 300 times. The spinner landed on a shaded region 168 times, so the experimental probability $P_{experimental}$ is: $$P_{experimental} = \frac{168}{300}$$ We simplify this fraction: $$P_{experimental} = \frac{\cancel{168}}{\cancel{300}} = \frac{56}{100} = 0.56$$ 4. **Compare the probabilities:** The theoretical probability is 0.625, and the experimental probability is 0.56. 5. **Conclusion:** The theoretical probability (0.625) is higher than the experimental probability (0.56). **Final answer:** The higher probability is the theoretical probability, which is 0.625.