# Probability Formulas

Probability formulas for everyday use…

P(event A or event B or both):

$P\left( A\cup B \right)$

P(both events A and B):

$P\left( A\cap B \right)$

P(not event A):

$P\left( A$

$P\left( A\cup B \right) =P\left( A \right) +P\left( B \right) -P\left( A\cap B \right)$

Multiplication rule:

$P\left( A\cap B \right) =P\left( { A }|{ B } \right) \times P\left( B \right)$

Conditional probability:

$P\left( { A }|{ B } \right) =\frac { P\left( A\cap B \right) }{ P\left( B \right) }$

Complementary probability:

$P\left( A$

A and B are mutually exclusive when:

$P\left( A\cap B \right) =0$

A and B are independent when:

$P\left( { A }|{ B } \right) =P\left( A \right)$

or…

$P\left( A\cap B \right) =P\left( A \right) \times P\left( B \right)$