1. Bell Work Determine the total number of outcomes (combinations). 1) You are picking an outfit from the following list of clothes. If you choose one hat, one shirt, one pair of pants, and one pair of socks, how many total outfits could you make? HatsShirtsPantsSocks Blue Green Yellow Black Pink Neon Green Striped Jeans Corduroys Polk-a-dot “Bacon” Rainbow Toe-socks Total Number of Hat Options: 4 Total Number of Shirt Options: 3 Total Number of Pants Options: 2 Total Number of Socks Options: 3 4 x 3 x 2 x 3 =72 72 Outfits!

2. Tree Diagrams, Organized Lists, and Tables Video

3. Tree Diagrams Way of organizing and visualizing outcomes Useful when the experiment happens in stages They can help you calculate probabilities

4. How many different ways can a red, blue and green marble be pulled from a bag? Solve using a Tree Diagram

5. How many different ways can a red, blue and green marble be pulled from a bag? Chance Experiment: Sample Space: Total Number of Outcomes: 1 2 3 4 5 6 Pulling a Marble from a bag Red, Blue, Green 6

6. How many different ways can a red, blue and green marble be pulled from a bag? Try making an organized list (R,B,G) (R,G, B) (G, R, B) (G, B, R) (B, G, R) (B, R, G)

7. HHHT THTT H T HTHT Making a Table You flip a coin twice. Make a table to display your outcome. Why can’t we can’t we use this method for the problem where we draw marbles out of a bag?

8. What is the probability of getting green, blue and red in that order? P(g, b, r)=

9. Independent and Dependent Events Tell whether the events are independent or dependent. You randomly draw a number from a bag. Then you randomly draw a second number without putting the first number back. b. You roll a number cube. Then you roll the number cube again. a. The result of the first roll does not affect the result of the second roll, so the events are independent. There is one fewer number in the bag for the second draw, so the events are dependent.

10. You Try In Exercises 1 and 2, tell whether the events are independent or dependent. Explain your reasoning. 1. You toss a coin. Then you roll a number cube. You randomly choose 1 of 10 marbles. Then you randomly choose one of the remaining 9 marbles. 2. The coins toss does not affect the roll of a dice, so the events are independent. There is one fewer number in the bag for the second draw, so the events are dependent.

11. head tail First Coin Second Coin head tail head tail Peter tosses two coins. (a)Draw a tree diagram to show all possible outcomes. (b) Use your tree diagram to find the probability of getting (i) 2 Heads (ii) A head or a tail in any order. P(2 heads) = ¼ P(head and a tail or a tail and a head) = ½ Independent Events

12. 2 Independent Events. 3 Selections First Draw Second Draw red blue red blue red blue Third Draw You choose a colored chip and then replace it. Finish the tree diagram for the second and third draw.

13. Practice