5.2 Combining Events Objectives: By the end of this section, I will be able to… 1) Understand how to combine events using complement, union, and intersection. 2) Apply the Addition Rule to events in general and to mutually exclusive events in particular.

Complements What is P(4) with one die? What is P(4) with one die? What is P(not 4) with one die? What is P(not 4) with one die? These are considered complementary events. These are considered complementary events.

Complements If one event is called Event A, the complement is called A c. If one event is called Event A, the complement is called A c.

SINGLE EVENTS What is the p(face card) from a standard deck of cards? What is the p(hearts) from a standard deck of cards? 12/52 13/52

COMBINING EVENTS What is the p(face cards and hearts)? What is the p(face cards and hearts)? Make a Venn Diagram Make a Venn Diagram

FACE CARDS HEARTS Face Cards & Hearts SAMPLE SPACE (everything else) Event A = Face cards Event B = Hearts P(A) =P(A) = 12/52 P(B) =P(B) = 13/52 P(A and B) = 3/52 P(A or B) = 22/52

Probability Notation ShorthandNotation Written Out Venn Diagram not A AcAcAcAc Complement of A A and B A ∩ B Intersection of A and B A or B A U B Union of A and B

Mutually Exclusive Events Two events, A and B, that cannot occur at the same time. Two events, A and B, that cannot occur at the same time. Example: Fly a plane and drive a car at the same time (its impossible!) Example: Fly a plane and drive a car at the same time (its impossible!) KEY WORDS: OR, EITHER KEY WORDS: OR, EITHER p(A or B) = p(A) + p(B) p(A U B) = p(A) + p(B)

Spoiled Brats Tankle has been shopping around for a new HOT ROD!! The probability a customer will buy an JEEP is 0.23 and the probability that a customer will buy a BMW is Tankle has been shopping around for a new HOT ROD!! The probability a customer will buy an JEEP is 0.23 and the probability that a customer will buy a BMW is What is the probability that Matt will buy EITHER of these two Cars? What is the probability that Matt will buy EITHER of these two Cars? = 0.32

CRAPS Two dice are rolled. What is the probability that the sum of the dots is a 7 OR 11? Two dice are rolled. What is the probability that the sum of the dots is a 7 OR 11? 6/36 + 2/36= 8/36 = ,3 3,4 2,5 5,2 1,6 6,1 5,6 6,5

OVERLAPPING Events Addition Rule: Addition Rule: p(A or B) = p(A) + p(B) – p(A and B) SUBTRACT OUT THE OVERLAPPING PART OF THE EVENT! What is the p(Ace or Hearts)?

CARDS WHAT IS THE PROBABILITY OF SELECTING A RED CARD OR A KING FROM A STANDARD DECK OF CARDS? WHAT IS THE PROBABILITY OF SELECTING A RED CARD OR A KING FROM A STANDARD DECK OF CARDS? 26/52 + 4/52 – 2/52 = 28/52 = = /52 4/52

Try This One! The probability of a guard being chosen by Coach Godfrey to start the basketball game is 0.42 and the probability that she chooses a forward is The probability of a guard being chosen by Coach Godfrey to start the basketball game is 0.42 and the probability that she chooses a forward is Three out of every five players can play both positions on Coach Godfrey’s team. Three out of every five players can play both positions on Coach Godfrey’s team. What is the probability that a player chosen to start the game is a guard OR a forward? What is the probability that a player chosen to start the game is a guard OR a forward? /5 = 0.16