Estimating Probabilities (VCE SSCE Mathematical Methods): Flashcards

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Estimating probabilities
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Subjective probabilities

Probabilities based on personal experience or judgment

Relative frequency

Proportion of trials resulting in a particular event

Formula for relative frequency

occurrencestrials\frac{\text{occurrences}}{\text{trials}}

Convergence principle

More trials → relative frequency closer to true probability

Best sample size for probability estimates

Use the largest available sample size

Best estimate from multiple data sets

Combine all data sets to maximise number of trials

Simulation in probability

Imitate or model a random experiment

Area-based probability formula

specific areatotal area\frac{\text{specific area}}{\text{total area}}

Probability as long-run interpretation

Proportion of times an event will occur in the long run

Key issue with subjective probabilities

May not be reliable or verifiable; vary between people

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