5.2 Combining Events

Objectives:By the end of this section, I will beable 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(not 4) with one die?

These are considered complementary events.

𝟏𝟔𝟓𝟔

Complements

If one event is called Event A, the complement is called Ac.

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)?

Make a Venn Diagram

FACE CARDS

HEARTS

Face Cards

& Hearts

SAMPLE SPACE (everything else)

Event A = Face cardsEvent B = Hearts

P(A) = P(A) = 12/52P(B) =P(B) = 13/52P(A and B) = P(A and B) =

3/52P(A or B) = P(A or B) =

22/52

Probability NotationShorthan

d Notation Written OutVenn Diagram

not A Ac 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.

Example: Fly a plane and drive a car at the same time (its impossible!)

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 0.09.

What is the probability that Matt will buy EITHER of these two Cars?0.23 + 0.09 =

0.32

CRAPS 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

= 0.22

4,3 3,4 2,5 5,2 1,6 6,1

5,6 6,5

OVERLAPPING Events 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)?𝟒𝟓𝟐

+𝟏𝟑𝟓𝟐

−𝟏𝟓𝟐

𝟏𝟔𝟓𝟐

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 = 0.53846 = 0.54

26/524/52

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 0.34.

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?

0.42 + 0.34 - 3/5 =

0.16