sp 2015 tree diagrams and sample space. video 1 video 2

SP 2015

Tree Diagrams and Sample Space

Video 1

Video 2

http://www.virtualnerd.com/sat-math/arithmetic/probability-counting/sample-space-count-outcomes-using-tree

https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-probability-statistics/cc-7th-compound-events/v/tree-diagram-to-count-outcomes

Example: Travel CostsA group asks a travel agent to help them plan a trip from Atlanta to Chicago. The agent gives them three choices of transportation between the cities: airplane, train, bus. Once the group arrives in Chicago, they can take a hotel shuttle or a taxi to get to the hotel. How many possible choices for the entire trip has the travel agent given them?

Airplane (A)

Shuttle (S)

Taxi (T)

Bus (B)

Shuttle (S)

Taxi (T)

Rail/Train (R)

Shuttle (S)

Taxi (T)

Tree Diagrams can be written Left to Right or Top to Bottom

Airplane (A)

Shuttle (S)

Taxi (T)

Bus (B)

Shuttle (S)

Taxi (T)

Rail/Train (R)

Shuttle (S)

Taxi (T)

Airplane (A)

Shuttle (S) Taxi (T)

Bus (B)


Rail/Train (R)


Example: Travel6 ChoicesHow much would each choice cost?

Airplane ($875)

Shuttle ($40)

875+40=$915

Taxi ($60)

875+60=$935

Bus ($425)

Shuttle ($40)

425+40=$465

Taxi ($60)

425+60=$485

Rail/Train ($650)

Shuttle ($40)

650+40=$690

Taxi ($60)

650+60=$710

Method Cost for Group

Air $875

Bus $425

Rail/Train $650

Shuttle $40

Taxi $60

The corner restaurant offers lunch combos for $6. The combo comes with a sandwich, side and drink. The choices are:Sandwich: Ham, TurkeySides: Chips, Fruit, SaladDrinks: Soda, Tea, WaterCreate a tree diagram.

How many possible combinations?

Ham

Chips

Soda

Tea

Fruit

Soda

Tea

Salad

Soda

Tea

Turkey

Chips

Soda

Tea

Fruit

Soda

Tea

Salad

Soda

Tea

1st Child

2nd Child

3rd Child

Girl

Girl

Girl - GGG

Boy - GGB

Boy

Girl - GBG

Boy - GBB

Boy

Girl

Girl - BGG

Boy - BGB

Boy

Girl - BBG

Boy - BBB

Example Trees for probability

A family will have 3 children.Answer the following:

P(all girls)

P(all boys)

P(2 girls and 1 boy)

Example:Rolling aPair of DiceHow many

possible outcomes:

6 * 6 = 36

How many Doubles6

P(Double) = 6/36 = 1/6

1

1

1,1

2

1,2

3

1,3

4

1,4

5

1,5

6

1,6

2

1

2,1

2

2,2

3

2,3

4

2,4

5

2,5

6

2,6

3

1

3,1

2

3,2

3

3,3

4

3,4

5

3,5

6

3,6

4

1

4,1

2

4,2

3

4,3

4

4,4

5

4,5

6

4,6

5

1

5,1

2

5,2

3

5,3

4

5,4

5

5,5

6

5,6

6

1

6,1

2

6,2

3

6,3

4

6,4

5

6,5

6

6,6

sp 2015 tree diagrams and sample space. video 1 video 2

Documents