The sample space (omega) collectively exhaustive for the experiment mutually exclusive right scope ‘granularity’ The probability law assigns a probability to every event in the sample space satisfies the axioms of probability

Nonnegativity: P(A)>=0 for all A Additivity: If A and B are disjoint sets, then the probability of their union is the sum of the probabilities of the set. Normalization: P(omega)=1 All other equations relating to probability laws are ultimately derived from the above axioms.

A shift into a new, related sample space, with a new probability law The new law still satisfies the axioms of probability The definition on page 20 could be written in words, “Whatever even A occurs must occur within the event B, so B is now the entire sample space.” relative probabilities are maintained Alternatively, the conditional probability could be viewed as remaining on the same sample space omega, but normalized by B.

Partition the sample space into A1…An then P(B) is the probability of B found in each set Ai summed over all i This amounts to P(B) being a weighted average of P(B|Ai) summed over all i, with P(Ai) as the weighting factor

The probability of a series of events is the product of the probability of each event in the series, conditioned on the previous event

A way to infer the probability of an event Ai as a cause, out of i possible causes for event B, which has been observed. We want to know the probability of Ai|B B has been observed, so the probability of the B also falling within the event Ai should be the ratio of the the probability of B occurring and being in event Ai (i.e. P(A)*P(B|Ai)) to the probability of B occurring at all. Verifiable by the definition of conditional probability (see pg. 20 and pg 32).