## Laws of Probability

If A and B are mutually exclusive events\[P(A \cap B)=0, \: P(A \cup B)=P(A)+P(B)\]

Also, \[P(A | B)=0\]

.\[P(A | B)\]

means 'probability of A happening given that B has happened. If A and B are mutually excusive and A has happened, then of course B cannot happen.If A and B are independent events

\[P(A \cap B)=P(A) \times P(B)\]

.Also,

\[P(A | B)=P(A)\]

.This means that the probability of A happening does not depend on whether B has happened since A is independent of B.

\[P(A | B)=\frac{P(A \cap B)}{P(B)}\]

.Also,

\[P(A \cup B)=P(A)+P(B)-P(A \cup B)\]

.These last two statements are true for all events A and B, independent or not.

\[P(A')=1-P(A)\]

.This means that the probability of A not happening is one minus the probability of A happening.