Basic Set Operations

Note: Let the left circle correspond to the event A, and the right circle to the event B.

1.Complement: The complement of $A$ refers to every valid event that is not within $A$, and is written $\bar{A}$.

$P(\bar{A}) = 1 - P(A)$

$Area(Rectangle) - \frac{Area(left \ circle)}{Area(Rectangle)} = 1 - \frac{Area(Left \ Circle)}{Area(Rectangle)} = 1 - P(A)$

2.Intersection: The intersection refers to the overlap of two event regions. It is possible that some event falls under two event types, in which case it is on the range that both event types cover.

$P(A \cap B) = 1 - P(A^c \cap B) - P(A \cap B^c) - P(A^c \cap B^c)$

The probability of the intersection can also be written as $P(A,B)$

3.Union: The union of two event types A and B refers to the area of the event space where outcomes would fall into at least one of the two.

$P(A \cup B) = 1 - P(A^c \cap B^c)$