Non-Mutually Exclusive Events

Non-Mutually Exclusive Events

In events which aren't mutually exclusive, there is some overlap. When P(A) and P(B) are added, the probability of the intersection (and) is added twice. To compensate for that double addition, the intersection needs to be subtracted.

General Addition Rule

Always valid.

   P(A or B) = P(A) + P(B) - P(A and B)

Example 2:

Given P(A) = 0.20, P(B) = 0.70, P(A and B) = 0.15

	B	B'	Marginal
A	0.15	0.05	0.20
A'	0.55	0.25	0.80
Marginal	0.70	0.30	1.00

Interpreting the table

Certain things can be determined from the joint probability distribution. Mutually exclusive events will have a probability of zero. All inclusive events will have a zero opposite the intersection. All inclusive means that there is nothing outside of those two events: P(A or B) = 1.

	B	B'	Marginal
A	A and B are Mutually Exclusive if this value is 0	.	.
A'	.	A and B are All Inclusive if this value is 0	.
Marginal	.	.	1.00

"AND" or Intersections