Bayes' Formula

    Consider the problem of testing the emissions from a motor vehicle. In a certain state, 25% of all cars emit excessive amounts of pollutants. Iff the probability is 0.99 that a car emitting excessive amounts of pollutants will fail the state's vehicular emissions test, and the probability is 0.17 that a car not emitting excessive amounts of pollutants will nevertheless fail the test, what is the probability that a car that fails the test actually emits excessive amounts of pollutants?

    Calculate P(B₆|A). (Make a tree diagram)

    The above can be generalized into:

• Bayes' Theorem

• An Example

• Office 95's natural-language help system employs Bayes' Rule

• GENETIC EVIDENCE IN PATERNITY CASES

  Ye Banks and Bayes

    Independence

    If I roll a die and then select a card from an ordinary deck of cards, you would probably believe that the outcome of rolling the die does not influence the selection of a card, that is, these actions happen independent of each other. How do we describe this idea of independence using the laws of probability?

• Conditional Probability and Independence

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