1. SP 2015 Tree Diagrams and Sample Space

2. Video 1 Video 2

3. Example: Travel Costs A 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)

4. 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)

5. Example: Travel 6 Choices How 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 MethodCost for Group Air$875 Bus$425 Rail/Train$650 Shuttle$40 Taxi$60

6. The corner restaurant offers lunch combos for $6. The combo comes with a sandwich, side and drink. The choices are: Sandwich: Ham, Turkey Sides: Chips, Fruit, Salad Drinks: Soda, Tea, Water Create a tree diagram. How many possible combinations? HamChipsSodaTeaWaterFruitSodaTeaWaterSaladSodaTeaWaterTurkeyChipsSodaTeaWaterFruitSodaTeaWaterSaladSodaTeaWater

7. 1 st Child2 nd Child3 rd ChildGirl Girl - GGG Boy - GGBBoyGirl - GBGBoy - GBBBoyGirlGirl - BGGBoy - BGBBoyGirl - BBGBoy - 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)

8. Example: Rolling a Pair of Dice How many possible outcomes: 6 * 6 = 36 How many Doubles 6 P(Double) = 6/36 = 1/6 111,121,231,341,451,561,6212,122,232,342,452,5 62,6 313,123,233,343,453,563,6414,124,234,344,454,564,6515,125,235,345,455,5 65,6 616,126,236,346,456,566,6