To determine if Philippe's estimated probability is representative of the theoretical probability, we must compare the two probabilities.
Estimated probability from Philippe's simulation: $\frac{4}{10} = 0.4$
Theoretical probability of it raining tomorrow cannot be determined from the given information.
If we assume that the spinner is fair and equally likely to land on each outcome, then the theoretical probability of it raining tomorrow is $\frac{1}{2}$ or $0.5$ (assuming there are only two possible outcomes: rain or no rain).
Since Philippe's estimated probability from the simulation is $0.4$ and the theoretical probability is $0.5$, they are somewhat close but not exactly the same. Philippe's estimated probability is slightly lower than the theoretical probability. This could be due to random chance or if the spinner is not fair and does not accurately represent the true probabilities of raining and not raining.
In conclusion, Philippe's estimated probability is close to the theoretical probability but may not be entirely representative due to the limitations of the simulation and assumptions made.
Philippe used a spinner to perform $10$ trials to simulate the probability of it raining tomorrow. He observed $4$ outcomes that it will rain tomorrow.
Is Philippe’s estimated probability representative of the theoretical probability of it raining tomorrow? Explain why or why not.
Provide the estimated probability from Philippe’s simulation and the theoretical probability of it raining tomorrow.
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