Probability Basics - Ch7:271-279

Terminology

  • Chance event - something the decision-makers are uncertain about

    • < 1 possible outcome

  • Mutually exclusive - only one can happen not both

  • Collectively exhaustive - one of the possible outcomes must occur

Requirements of Probabilities

  1. Probabilities must lie between 0 and 1 (inclusive)

    1. i.e. nothing can have more than a 100% chance of occurring or less than a 0% chance

  2. Probabilities must add up

    1. 2 mutually exclusive outcomes = the probability that one occurs is the sum of the individual probabilities

  3. Total probability must equal 1

    1. when an outcome set is CEME, the set probabilities must add up to 1

  • seen in decision trees - only one of the branches terminating from a chance node can occur and all branches sum to 1

Probability Formulas

  1. Conditional probability - the probability of an event occurring given that another event has already occurred

    1. P(A|B) = P(A and B)/ P(B) = probability of A given B

  2. Independence - The occurrence of one event doesn’t affect the probability of another occurring

  3. Conditional independence - 2 events are considered independent of each other once a third event is known to have occurred

    1. P(A|BC) = P(A|C)

  4. Complements - if B does not occur, then B-bar must occur

    1. P(B-bar) = 1 - P(B)

  5. Total probability of an event - overall likelihood an an event occurring, calculated bt summing the probabilities of all possible ME paths that could lead to an event happening

  6. Bayes’ Theorem - used to reorder chance nodes

    1. Formula

PrecisionTree and Bayes’ Theorem

  • PrecisionTree tool can automatically reorder chance nodes and apply Bayes Theorem