Outcomes are mutually exclusive if they cannot happen at the same time

Example: rolling dice once and getting 6 and 2

The Addition Rule of Probability

Mutually Exclusive Events (Disjoint)

The Addition Rule of Probability

Not Mutually Exclusive Events (Not Disjoint)

More complicated OR

• To the right you see cards that can each be described in two ways

• Jack, Queen, King or Ace

• Heart, Club, Diamond or Spade

• So, one card can be two things at once, for example a Queen and a Heart.

More complicated OR

• When we talk about OR probabilities we have to take "double identity" into account

• P(Queen or Heart) seems simple... just add the Queen probability to the Heart probability.... BUT

• What about the Queen of Hearts? It will get counted twice, so....

• We will have to consider OR and take away AND to get rid of the double count

More complicated OR

• P(A or B) = P(A) + P(B) - P(AB)

• P( Queen OR Heart) = P(Queen) + P(Heart) - P(Queen of Hearts)

• P(Queen or Heart) = 4/16 + 4/16 - 1/16

• P(Queen or Heart) = 7/16

• In this simple example we can count the cards shown to see this is true!