Section 5.2The Addition Rule and Complements

KEY IDEA

All disjoint events in a sample space sum to

1

• Two events are disjoint if they have no outcomes in common.

• Disjoint events are also called mutually exclusive events.

• Example: Toss a coin. H and T are disjoint.• Example: Roll a die. 1,2,3,4,5,6 are disjoint.• Example: Roll a die. The events E={1,2,3} and

F={4,5,6} are disjoint.• Example: Roll a die. The events E={1,2,3} and

F={2,4,6} are not disjoint. They share {2}.

Venn DiagramsUsed to display simple probability logic.But requires special software to draw on computer.

Let S=sample space={1,2,3,4,5,6,7,8,9,10}A={1,2,3,4,10), B={4,5,6,7,9}

“Union of A and B” = A or B = A U B = { 1, 2, 3, 4, 5, 6, 7, 9, 10 }

“Intersection of A and B” = A and B = A ∩ B = { 4 }

“Not A” = complement of A = AC = {5, 6, 7, 8, 9}

Addition Rule for Disjoint EventsP(A or B) = P(A U B) = P(A) + P(B)

IF A and B are disjoint events

For non-disjoint and disjoint eventsP(A U B) = P(A) + P(B) – P(A∩B)

Notice 1: P(A)+P(B) counts intersection twice.Notice 2: If A and B are disjoint, P(A∩B)=0.

Complement RuleP(AC)=1-P(A)

Show P(A U B) = P(A) + P(B) – P(A∩B)

P(A and C) = ?P(A or C ) = ?P(A and B) = ?P(A or B) = ?P(A or B or C)=?

From a 52 card deck, what is P( Spades or King)?