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Let’s Review. If two events are independent…. * P ( A ∩ B ) = P ( A ) P ( B ) * P ( B | A ) = P ( B ) *P ( A | B ) = P ( A ) *They cannot be mutually exclusive!. If two events are dependent…. * P ( A ∩ B ) = P ( A ) P ( B | A ) * P ( B | A ) ≠ P ( B )

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If two events are independent
If two events are independent…

*P(A ∩ B) = P(A) P(B)

*P(B | A) = P(B)

*P(A| B) = P(A)

*They cannot be mutually exclusive!


If two events are dependent
If two events are dependent…

*P(A ∩ B) = P(A) P(B | A)

*P(B | A) ≠ P(B)

*P(A| B) ≠P(A)


If two events are mutually exclusive
If two events are mutually exclusive…

*P(A U B) = P(A) + P(B)

*P(B ∩ A) = 0

*They cannot be independent!


Venn diagrams
Venn Diagrams…

The green shaded area is the union.

The green shaded area is the intersection.



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