Quantitative Analysis

The set of all possible outcomes of a random experiment. An event is any subset of the sample space.

They cannot both occur, so their intersection is empty and P(A∩B)=0. The occurrence of one rules out the other.

P(A∪B) = P(A) + P(B) − P(A∩B). The intersection is subtracted to avoid double-counting; for mutually exclusive events it reduces to P(A)+P(B).

P(A|B) = P(A∩B)/P(B), valid for P(B)>0. It is the probability of A given that B has occurred.

P(A∩B) = P(A|B)·P(B) = P(B|A)·P(A). It follows directly from the definition of conditional probability.

When P(A∩B) = P(A)P(B), equivalently P(A|B)=P(A). Knowing B occurred does not change the probability of A.