Probability(C14-C17 BVD) C15: Probability Rules

* OR – In probability language, OR means that either event happening or both events happening in a single trial is considered a “success”. * P(red or green) = P(red) + P(green) – P( any double-counted overlap) * Venn Diagrams make these General Addition Rule problems MUCH easier.

* Conditional Probability * P(A|B) = P(A given B) = P(A on condition that B happens) * P(A|B) = P(A and B) / P(A) * If you have a contingency (two-way) table, it is typically easy to just find values in table: * P(A and B) is the box in table where both are true * P(A) in table is the total for event A in the table

* P(this and that) = P(this) * P(that) if events are independent. * If this and that are NOT independent, the probably P(that) is changed once this occurs. => * P(this and that) = P(this)*P(that|this) – generalized multiplication rule

* If the probability P(that|this) is the same as P(that), then it is not changed given that this occurs. * This means the two events are independent events. * Caution: Independent does NOT mean disjoint/mutually exclusive. Mutually exclusive events cannot be independent – knowing that one occurred means the other one definitely did not, i.e. the probability of one of them changed to zero given that the other happened.

* Be careful about wording. P(A and B), P(A|B) and P(B|A) are all different. * Lets say you know the probability of a random person having HIV, and you know the probabilities of positive test results for people who do and do not have HIV. If you make the tree diagram, you can also find: * 1. P(HIV and + test) and other such combinations by multiplying “branches” * 2. P(HIV|+) or P(HIV|-) etc. using the conditional probability formula – (these are reserved conditioning, because in making the tree you knew P(+|HIV) and so on, but not the other way around.) * See example pages for reversing conditioning examples.