1. Unit 8. Day 6.

2. Today we will review “tree diagrams”
You may have already seen tree diagrams (maybe not applied to probability)
This easy idea will be used to remind us of the a “trick”
Then we will use tree diagrams & the “trick” to help us find probabilities of compound events.
CCSS.MATH.CONTENT.7.SP.C.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

3. Example A: Gabi is packing for a trip
Example A: Gabi is packing for a trip. She has 4 tops, 3 bottoms, and 2 pairs of shoes. How many different outfits can she make?

4. There must be a better way!
Example A: Gabi is packing for a trip. She has 4 tops, 3 bottoms, and 2 pairs of shoes. How many different outfits can she make? 𝑆=
𝑇1 𝐵1 𝑆1
𝑇2 𝐵1 𝑆1
𝑇1 𝐵1 𝑆2
𝑇2 𝐵1 𝑆2
𝑇1 𝐵2 𝑆1
𝑇1 𝐵2 𝑆2
𝑇1 𝐵3 𝑆1
𝑇1 𝐵3 𝑆2
This is crazy!
There must be a better way!

5. Example A: Gabi is packing for a trip
Example A: Gabi is packing for a trip. She has 4 tops, 3 bottoms, and 2 pairs of shoes. How many different outfits can she make? 𝑇1 𝑇2 𝑇3 𝑇4 𝐵1 𝐵3 𝐵1 𝐵2 𝐵3 𝐵2 𝐵1 𝐵2 𝐵3 𝐵1 𝐵2 𝐵3 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2

6. Example A: Gabi is packing for a trip
Example A: Gabi is packing for a trip. She has 4 tops, 3 bottoms, and 2 pairs of shoes. How many different outfits can she make?
Multiplying “trick”: 4 ∙ 3 ∙ 2 = 24

7. Strawberry Strawberry
Example B: An ice cream shop has 2 types of cones, 4 flavors, & 2 toppings. How many different ice cream cones can be made ?
Waffle
Mango
Chocolate
Waffle
Mango
Strawberry
Waffle
Vanilla
Chocolate
Waffle
Vanilla
Strawberry
Waffle
Mint CC
Chocolate
Waffle
Mint CC
Strawberry
Waffle
Chocolate
Chocolate
Waffle
Chocolate
Strawberry
Sugar
Mango
Chocolate
Sugar
Mango
Strawberry
Sugar
Vanilla
Chocolate
Sugar
Vanilla
Strawberry
Sugar
Mint CC
Chocolate
Sugar
Mint CC
Strawberry
Sugar
Chocolate
Chocolate
Sugar
Chocolate
Strawberry

8. Multiplication: 2 ∙ 4 ∙ 2 = 16 Waffle Sugar Mango Vanilla Mint CC
Chocolate
Mango
Strawberry
Chocolate
Vanilla
Strawberry
Waffle
Chocolate
Mint CC
Strawberry
Multiplication:
Chocolate
Chocolate
Strawberry 2 ∙ 4 ∙ 2 = 16
Chocolate
Mango
Strawberry
Chocolate
Vanilla
Sugar
Strawberry
Chocolate
Mint CC
Strawberry
Chocolate
Chocolate
Strawberry

9. Example C: A car comes with the choice of gas or diesel engines, automatic or manual transmissions, and cloth or leather seats. The car has five different colors: white, green, red, silver, black. How many different cars are there? w g r s b w g r s w b g r w s b g r s w b g r s w b g r s w b
Multiplication: g r s w b g 2 ∙ 2 ∙ 2 = 40 r ∙ 5 s b

10. Examples A, B, and C were not random/chance events.
In 7th grade we use tree diagrams to find sample spaces & probabilities of chance events

11. Example D: Carnival Game.𝑆= 𝑅 𝐵 𝐵 𝑅 𝐵 𝑅 𝐵 𝑅 𝑅 𝐵 𝑌 𝐺 𝐵 𝑅 𝑌 𝐺

12. Example D: Carnival Game
𝑅𝑒𝑑
𝐵𝑙𝑢𝑒
𝑅𝑒𝑑
𝐵𝑙𝑢𝑒
𝑌𝑒𝑙𝑙𝑜𝑤
𝐺𝑟𝑒𝑒𝑛
𝑅𝑒𝑑
𝐵𝑙𝑢𝑒
𝑌𝑒𝑙𝑙𝑜𝑤
𝐺𝑟𝑒𝑒𝑛

13. Example E: A dice is rolled twice?1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 9
1 4
𝑃 𝑏𝑜𝑡ℎ 𝑟𝑜𝑙𝑙𝑠 𝑎𝑟𝑒 𝑜𝑑𝑑 = = 36

14. Example F: A coin is flipped 4 times
Example F: A coin is flipped 4 times. What is the probability of getting at least three heads? 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 𝐻 𝑇 5
𝑃 𝐻≥3 = 16