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Probability
by Jane_l Yang
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Probability

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Random Circumstance

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outcome not determined until we see it

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Outcome already determined but our knowledge is uncertain

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Relative Frequency Interpretation

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Make assumption about Physical world

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Make direct observation of how often something happens over many, many repetitions of the situation.

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Number between 0 and 1

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The possible outcome of a random circumstance

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Meets 1st condition for valid probablity

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Personal Probability (subjective)

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Degree an individual believes it will happen

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Coherent (no contradiction)

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Uses percentages based on proportions of individuals

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Definitions

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Sample Space

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Simple Event

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Event

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Events

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Complementary ("Opposite")

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mutually exclusive (disjoint)

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Independent

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Dependent

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Conditional Probablity

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Rules for Finding Probabilities

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Rule 1 (Not the event)

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Rule 2 (Addition)

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Rule 3 (Multiplication)

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Rule 4 (Conditional Probability)

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Philosophical Issue

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Outcome has been determined but is still unknown

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Confidence vs Probability

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Strategies

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Bayes Rule

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Two-way Tables: Hypothetical 100,000

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Tree Diagram

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The proportion of times something would occur over the long run.