Warm Up – Thursday 9/24 Find the simplified form of 5 3x 2x2x +

Lesson 1.2Counting Outcomes & Tree Diagrams (Text 12.2) Tree Diagram A diagram that shows possible outcomes of an event

Example 1ATree Diagrams Suppose you have 2 different toys you receive in your box of Lucky Charms cereal. Find the probability that you will receive Both two within buying two boxes cereal? Box 1 Box 2 Toy 1 Toy 2 Toy 1 Toy 2 Toy 1 Toy 2

Example 1BTree Diagrams Suppose you have 3 different toys you receive in your box of Lucky Charms cereal. Find the probability that you will receive All three toys within buying 3 boxes cereal? See Textbook for diagram

Fundamental Counting Principal Event M can occur m way and N occurs n ways. The total number of outcomes of event M followed by N is m∙n. (Note: The order matters) Example 2AFCP Suppose you have 5 SMOD shirts, 3 SMOD pants, and two pairs of shoes to choose from. How many potential outfits might you Put together without repeating an outfit? ShirtsPantsShoes Days

Example 2BFCP Mr. Jones has 10 girls on his AAU basketball team. Jenny will play Center, and the remaining 9 girls may fill any of the other positions. How many lineups might he choose? Lineups CenterG1G2 F1F2 76

Example 2CFCP How many North Carolina license plates like the one show may be Uniquely created? ,760,000 Plates 10 L1L2L3 N1N2 N3N4 10

“and” Rule for Probability Example 3A“and Rule” Independent Events Suppose you draw one card at a time (with replacement) from a standard deck of playing cards? What is the probability of drawing an ace followed by spade? AceSpade If event A is followed event B, P(A and B) = P(A) P(B)

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

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

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

Example

Example 6