W8: Reasoning with Uncertainty

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8 Terms

1
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What are the rules of probabilities of complex outcomes?

  1. Tautologies get assigned 1. Contradictions get assigned 0

  2. Disjunctions “V” (or) = Union (∪)

  3. Conjunctions “&” = Intersection (∩)


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Rule 2: What is the formula for P(A V B)?

P(A V B) = P(A) + P(B) - P(A&B)

3
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Rule 2: Suppose A and B are mutually exclusive (cannot happen at the same time), what is P(A V B)?

P(A V B) = P(A) + P(B)

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Rule 3: What is the formula for P(A & B)?

P(A & B) = P(A) x P(B)

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Only under what condition will this formula hold?

If A and B are independent outcomes

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If A and B are dependent, what do we use?

Conditional probabilities: P(A & B) = P(A) x P(B|A)

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How would the probability look like for P(at least one heads) for two dice throws?

P(at least one H) = P(H1 V H2)

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What is the gambler’s fallacy?

The false belief that past, independent outcomes can influence future outcomes

e.g. landing on heads many times does not make landing on tails next more probable)