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.
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?
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 𝐵1 𝑆1 𝑇2 𝐵1 𝑆1
𝑇1 𝐵1 𝑆2 𝑇2 𝐵1 𝑆2
𝑆=
𝑇1 𝐵2 𝑆1
𝑇1 𝐵2 𝑆2
𝑇1 𝐵3 𝑆1
𝑇1 𝐵3 𝑆2
This is crazy!
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?
𝑇2
𝑇1
𝐵1
𝐵2 𝐵3
𝐵1
𝐵2 𝐵3
𝑇3
𝐵1
𝐵2
𝑇4
𝐵3 𝐵1 𝐵2 𝐵3
𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1 𝑆2 𝑆1𝑆2 𝑆1𝑆2 𝑆1𝑆2
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
Example B: An ice cream shop has 2 types of cones, 4 flavors, &
2 toppings. How many different ice cream cones can be made ?
Mango
Waffle
Chocolate
Mango
Waffle
Strawberry
Vanilla
Waffle
Chocolate
Vanilla
Waffle
Strawberry
Waffle
Mint CC
Chocolate
Waffle
Mint CC
Strawberry
Waffle
Chocolate
Chocolate
Waffle
Chocolate
Strawberry
Mango
Sugar
Chocolate
Mango
Sugar
Strawberry
Vanilla
Sugar
Chocolate
Vanilla
Sugar
Strawberry
Sugar
Mint CC
Chocolate
Sugar
Mint CC
Strawberry
Sugar
Chocolate
Chocolate
Sugar
Chocolate
Strawberry
Mango
Vanilla
Waffle
Multiplication:
2∙ 4 ∙
Chocolate
Strawberry
Chocolate
Strawberry
Mint CC
Chocolate
Strawberry
Chocolate
Chocolate
Strawberry
2 = 16
Mango
Sugar
Chocolate
Strawberry
Mint CC
Chocolate
Strawberry
Chocolate
Strawberry
Chocolate
Chocolate
Strawberry
Vanilla
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?
Multiplication:
2 ∙ 2 ∙ 2 ∙ 5 = 40
wg
r
bs
wg
r
bwsg
r
sg
bw
r
wgb s
r
wbgs
r
wbgs
r
wbgs
r
bs
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
Example D: Carnival Game.
𝑆=
𝑅
𝑅
𝑅
𝑅
𝐵
𝐵
𝐵
𝐵
𝑅
𝑅
𝐵
𝐵
𝐺
𝐺
𝑌
𝑌
Example D: Carnival Game
𝐵𝑙𝑢𝑒
𝑅𝑒𝑑
𝑅𝑒𝑑
𝐵𝑙𝑢𝑒
𝑌𝑒𝑙𝑙𝑜𝑤
𝐺𝑟𝑒𝑒𝑛
𝑅𝑒𝑑 𝐵𝑙𝑢𝑒 𝑌𝑒𝑙𝑙𝑜𝑤 𝐺𝑟𝑒𝑒𝑛
Example E: A dice is rolled twice?
1
2
1 23 4 56 1 2345 6
3
4
5
6
1 23 45 6 12 3 4 56 1234 56 12 3 4 5 6
𝑃 𝑏𝑜𝑡ℎ 𝑟𝑜𝑙𝑙𝑠 𝑎𝑟𝑒 𝑜𝑑𝑑 =
9
36
=
1
4
Example F: A coin is flipped 4 times. What is the
probability of getting at least three heads?
𝐻
𝑇
𝐻
𝑇
𝐻
𝐻
𝑇
𝐻
𝑇
𝐻𝑇
𝐻𝑇
𝐻𝑇
𝐻𝑇
𝐻
𝑇
𝑇
𝐻𝑇 𝐻 𝑇
5
𝑃 𝐻≥3 =
16
𝐻
𝑇
𝐻𝑇 𝐻 𝑇