Warm Up – Thursday 9/24

Find the simplified form of

53x

2x

+

Lesson 1.2 Counting Outcomes & Tree Diagrams (Text 12.2)

Tree Diagram A diagram that shows possible outcomesof an event

Example 1A Tree DiagramsSuppose you have 2 different toys you receive in your box of Lucky Charms cereal. Find the probability that you will receiveBoth two within buying two boxes cereal?

Box 1 Box 2

Toy 1

Toy 2

Toy 1

Toy 2

Toy 1

Toy 2

Example 1B Tree DiagramsSuppose you have 3 different toys you receive in your box of Lucky Charms cereal. Find the probability that you will receiveAll three toys within buying 3 boxes cereal?

See Textbook for diagram

Fundamental Counting PrincipalEvent M can occur m way and N occurs n ways. The total numberof outcomes of event M followed by N is m n. ∙(Note: The order matters)

Example 2A FCPSuppose you have 5 SMOD shirts, 3 SMOD pants, and two pairsof shoes to choose from. How many potential outfits might youPut together without repeating an outfit?

• •

Shirts Pants Shoes

5 3 2 30 Days

Example 2B FCPMr. Jones has 10 girls on his AAU basketball team. Jenny will playCenter, and the remaining 9 girls may fill any of the other positions.How many lineups might he choose?

1 9 8 3024 Lineups• •

Center G1 G2

• •

F1 F2

7 6

Example 2C FCPHow many North Carolina license plates like the one show may beUniquely created?

26 26 26

175,760,000 Plates

10• •

L1 L2 L3

• •

N1 N2

• •

N3 N4

10 10 10

“and” Rule for Probability

Example 3A “and Rule” Independent EventsSuppose you draw one card at a time (with replacement) froma standard deck of playing cards? What is the probability of drawing an ace followed by spade?

•

Ace Spade

If event A is followed event B, P(A and B) = P(A) • P(B)

524

5213

%9.1521

Example 3B “and Rule” Independent EventsSuppose you draw one marble at a time (with replacement) fromA bag containing 5 white, 6 red, and 9 blue? What is the probability of drawing an white and then a blue marble?

•

White Blue

205

209

%25.11809

Example 4A “and Rule” Dependent EventsSuppose you draw one card at a time (without replacement) froma standard deck of playing cards? What is the probability of drawing an ace followed by a king?

•

Ace king

524

514

%6.06634

Example 4B “and Rule” Dependent EventsSuppose you draw one marble at a time (without replacement) fromA bag containing 8 white, 2 red, and 10 blue? What is the probability of drawing an white and then another white?

•

White White

208

197

%7.149514

Example 5

.68

.94

.06.0408

.08

.92.2944

Example 6