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

Addition rule:

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) 


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