Probability Formulas

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P A( ) =#of ways A can happen

# items in the sample space for event A

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P A∪B( ) = P A( ) + P B( )

The probability of more than one outcome.This is a union of the probabilities.

If events are disjoint:

If events are not disjoint:

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P A∪B( ) = P A( ) + P B( ) − P A∩ B( )

Means the intersection of A and B.The number of items events A and B have in common.

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P A∩ B( )

Probability of more than one event. The probability of both A and B happening.

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P A∩ B( ) = P A( ) ⋅ P B( )

If A and B are independent:

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P A∩ B( ) = P A( ) ⋅ P B A( )

If A and B are not independent:

means the probability of B given that A has already happened.

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P B A( )

Conditional Probabilities

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P A B( ) =P A∩ B( )P B( )

The probability of A given B.

The probability of B given A.

The intersection (overlap) of A and B divided by B.

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P B A( ) =P A∩ B( )P A( )

The intersection (overlap) of A and B divided by A.

Definition of Independent Events

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P A( ) = P A B( )

Events A and B are independent if either of the following are true:

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P B( ) = P B A( )

Practice #17 p. 363 23 – 35 odds, 41, 45