sp 2015 tree diagrams and sample space. video 1 video 2
TRANSCRIPT
SP 2015
Tree Diagrams and Sample Space
Video 1
Video 2
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)
Shuttle (S) Taxi (T)
Rail/Train (R)
Shuttle (S) Taxi (T)
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
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1,3
4
1,4
5
1,5
6
1,6
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1
2,1
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2,2
3
2,3
4
2,4
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2,5
6
2,6
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1
3,1
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3,2
3
3,3
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3,4
5
3,5
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3,6
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1
4,1
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4,2
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4,3
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4,4
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4,5
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4,6
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1
5,1
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5,2
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5,3
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5,4
5
5,5
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5,6
6
1
6,1
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6,2
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6,3
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6,4
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6,5
6
6,6