Section #1

1. Section #1 For each example, draw a tree diagram labeling each “level” or event out to the left of the diagram. EX: Flipping a penny and flipping a quarter Start Flipping a penny Heads Tails Flipping a quarter Heads Tails Heads Tails

2. Section #1 Start Heads Tails Heads Tails Heads Tails When the diagram is complete, use it to create a list of your sample space (all of your possible outcomes.) Sample Space: S = {HH, TH, HT, TT}

3. Section #1 Possible outcomes flipping penny: { } Possible outcomes flipping quarter: { } Sample Space: S = { # of possible outcomes flipping penny:_____# of possible outcomes flipping quarter:____ Total number of outcomes in the sample space:____ Heads, Tails Heads, Tails HH, TH, HT, TT} 2 2 4

4. Section 2: EX: Using numbers 1-10, find P(odd or greater than 7) List all of the odd numbers in the set : { }List all numbers in the set greater than 7: { } How many odd #’s are in the set?____How many #’s in the set are greater than 7?____ How many #’s in the set are both odd andgreater than 7 at the same time?_____ (Circle them) 1, 3, 5, 7, 9 8, 9, 10 5 3 1

5. In Section #1: EX1 Possible outcomes at 1st stoplight: { } Possible outcomes at 2nd stoplight: { } Possible outcomes at 3rd stoplight: { } Sample Space: S = { Red, Green, Yellow Red, Green, Yellow Red, Green, Yellow RRR, GRR, YRR, RGR, GGR, YGR, RYR, GYR, YYR, RRG, GRG, YRG,RGG, GGG, YGG, RYG, GYG, YYG, RRY, GRY, YRY, RGY, GGY, YGY, RYY, GYY, YYY}

6. In Section #1: EX1 3 # of possible outcomes at 1st stoplight: ________ # of possible outcomes at 2nd stoplight: _______ # of possible outcomes at 3rd stoplight: ________ Total number of outcomes in the sample space: _______ 3 3 27

7. In Section #1: EX2 Possible outcomes when picking a number: { } Possible outcomes when flipping a coin: { } Sample Space: S = { 1, 2, 3, 4, 5 Heads, Tails 1T, 1H, 2T, 2H, 3T, 3H, 4T, 4H, 5T, 5H, 6T, 6H}

8. In Section #1: EX1 5 # of possible outcomes when picking a number: ________ # of possible outcomes flipping a coin: _______ Total number of outcomes in the sample space: _______ 2 10

9. In Section #1: EX1 How can you use the number of outcomes of each event (or level in the tree diagram to find the total number of possible outcomes in a sample space? Multiply the number of outcomes For each event together

10. Finding Total Number of Outcomes Multiply the number of possible outcomes at each “level” of the tree diagram.

11. Finding Total Number of Outcomes Example: Lindsay is getting ready for school. She has three shirts, 4 pairs of pants and 3 pairs of shoes to choose from. How many possible outcomes could she have for an outfit of one shirt, one pair of pants and one pair of shoes?

12. Finding Total Number of Outcomes Example: Number of shirts = 3 Number of pants = 4 Number of shoes = 3 Total number of outcomes: 3 * 4 * 3 = 36

13. Section 2 EX1: EX: Using a deck of cards, find P(4 or 6) List all of the 4’s: { }List all of the 6’s: { } How many 4’s are in the deck?____How many 6’s are in the deck?____ How many cards are both a 4 and a 6 at the same time?_____(Circle them) 4 4 0

14. Section 2 EX2: EX: Using a deck of cards, find P(Ace or clubs) List all of the Ace’s: { }List all of the Clubs: { } How many Ace’s are in the deck?____How many clubs are in the deck?____ How many cards are both a 4 and a 6 at the same time?_____(Circle them) 4 13 1

15. Section 2 EX3: EX: Rolling a die, find P(greater than 2 or even) List all of the numbers greater than 2: { }List all of the even numbers: { } How many #s are greater than 2?____How many #s are even?____ How many cards are both greater Than 2 or even?____(Circle them) 3, 4, 5, 6 2, 4, 6 4 3 2

16. Section 2 EX4: EX: Rolling a die, find P(less than 3 or greater than 4) List all of the numbers less than 3: { }List all of the numbers greater than 4: { } How many #s are less than 3?____How many #s are greater than 4?____ How many cards are both less than 3 Or greater than 4?____(Circle them) 1, 2 5, 6 2 2 0

17. Mutually Exclusive Two events are mutually exclusive if they cannot occur at the same time *They have no outcomes in common

18. Are they Mutually Exclusive? Which of the following are mutually exclusive? • Getting a 7 and getting a jack • Getting a club and getting a king • Getting a face card and getting an ace • Getting a face card and getting a spade A and C are mutually exclusive

19. P(A or B) for Mutually Exclusive When two events A and B are mutually exclusive, the probability that A or B will occur is: P(A or B) = P(A) + P(B)

20. Given a deck of cards, find P(jack or a 7): P(jack or a 7) = P(jack) + P(7) = 4/52 + 4/52 = 8/52 = 2/13

21. Mutually Exclusive Venn Diagram P(jack or a 7) Jack 7

22. P(A or B) for NOT Mutually Exclusive If A and B are NOT mutually exclusive (they have an outcome in common) then the probability that A or B will occur is: P(A or B) = P(A) + P(B) – P(A and B)

23. Given a deck of cards, find P(heart or ace): P(heart or ace) = P(heart) + P(ace) – P(heart and ace) = 13/52 + 4/52 – 1/52 = 16/52 = 4/13

24. NOT Mutually Exclusive Venn Diagram P(heart or ace) Heart Ace